By the end of this chapter, you will be able to:
Mastering these skills will help you manage building projects confidently and ensure fair, accurate, and safe handling of all tendering and appraisal tasks in your trade.
Compiled by: John Wachira
Project appraisals are critical in building technology projects to determine the feasibility, cost-effectiveness, and potential returns of proposed construction works. For building professionals in Kenya, preparing accurate project appraisals informs decision-making for stakeholders such as developers, banks, and government agencies. This chapter focuses on the key items required in project appraisals to enable comprehensive evaluation of building projects before investment or commencement.
Project appraisal items encompass all the quantitative and qualitative factors considered when evaluating a building project. These items allow professionals to assess costs, benefits, risks, and other essential metrics. Understanding and calculating these items accurately is vital to producing reliable project appraisals that guide investment and implementation decisions.
Preliminary cost estimates provide an initial approximation of the total project expenditure based on early design concepts or feasibility studies. These estimates use unit rates and approximate quantities to give a rough idea of the financial requirements before detailed designs are available.
The main formula used for preliminary cost estimates is:
$$ \text{Preliminary Cost} = \sum (\text{Quantity}_i \times \text{Unit Rate}_i) $$
Example 1: Estimate the preliminary cost of plastering walls in a hospital project given that the plastering area is 250 m² and the unit rate is Ksh 450 per m².
Given:
Quantity \(= 250\, m^2\)
Unit rate \(= 450\, Ksh/m^2\)
$$ \text{Preliminary Cost} = 250 \times 450 $$
$$ = 112,500\, Ksh $$
Answer: Preliminary cost = 112,500 Ksh
Example 2: A county office building requires roofing sheets for an area of 120 m². If the unit rate per m² is Ksh 1,200, estimate the preliminary cost.
Given:
Quantity \(= 120\, m^2\)
Unit rate \(= 1,200\, Ksh/m^2\)
$$ \text{Preliminary Cost} = 120 \times 1,200 $$
$$ = 144,000\, Ksh $$
Answer: Preliminary cost = 144,000 Ksh
Example 3: For a retail store, the preliminary cost of electrical installation is based on 80 points at a unit rate of Ksh 2,500 per point. Calculate the preliminary cost.
Given:
Quantity \(= 80\, \text{points}\)
Unit rate \(= 2,500\, Ksh/\text{point}\)
$$ \text{Preliminary Cost} = 80 \times 2,500 $$
$$ = 200,000\, Ksh $$
Answer: Preliminary cost = 200,000 Ksh
Example 4: A school project requires flooring for 300 m². The unit rate for tiling is Ksh 1,000 per m². Calculate the preliminary cost estimate.
Given:
Quantity \(= 300\, m^2\)
Unit rate \(= 1,000\, Ksh/m^2\)
$$ \text{Preliminary Cost} = 300 \times 1,000 $$
$$ = 300,000\, Ksh $$
Answer: Preliminary cost = 300,000 Ksh
Example 5: Estimate the preliminary cost of painting 400 m² of walls at a unit rate of Ksh 350 per m² for a cooperative headquarters.
Given:
Quantity \(= 400\, m^2\)
Unit rate \(= 350\, Ksh/m^2\)
$$ \text{Preliminary Cost} = 400 \times 350 $$
$$ = 140,000\, Ksh $$
Answer: Preliminary cost = 140,000 Ksh
Net Present Value (NPV) is a financial appraisal metric that calculates the present value of future cash flows generated by a building project, discounted at a specific rate. It helps determine whether the project's returns justify the initial investment.
The formula for NPV is:
$$ NPV = \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} - C_0 $$
Where:
\(C_t\) = cash inflow at year \(t\)
\(r\) = discount rate (decimal)
\(n\) = project duration in years
\(C_0\) = initial investment cost
Example 1: A retail store project requires an initial investment of Ksh 2,000,000. Expected cash inflows over 3 years are Ksh 800,000, Ksh 900,000, and Ksh 1,000,000. If the discount rate is 10%, calculate the NPV.
Given:
\(C_0 = 2,000,000\, Ksh\)
\(C_1 = 800,000\, Ksh\)
\(C_2 = 900,000\, Ksh\)
\(C_3 = 1,000,000\, Ksh\)
\(r = 0.10\)
\(n = 3\)
$$ NPV = \frac{800,000}{(1+0.10)^1} + \frac{900,000}{(1+0.10)^2} + \frac{1,000,000}{(1+0.10)^3} - 2,000,000 $$
$$ = \frac{800,000}{1.10} + \frac{900,000}{1.21} + \frac{1,000,000}{1.331} - 2,000,000 $$
$$ = 727,273 + 743,802 + 751,315 - 2,000,000 $$
$$ = 2,222,390 - 2,000,000 $$
Answer: NPV = 222,390 Ksh
Example 2: A hotel project has an initial cost of Ksh 10,000,000. Cash inflows over 4 years are Ksh 3,000,000 annually. Discount rate is 12%. Calculate the NPV.
Given:
\(C_0 = 10,000,000\, Ksh\)
\(C_t = 3,000,000\, Ksh\) for \(t=1\) to 4
\(r = 0.12\)
\(n = 4\)
$$ NPV = \sum_{t=1}^{4} \frac{3,000,000}{(1+0.12)^t} - 10,000,000 $$
Calculate each term:
$$ \frac{3,000,000}{1.12} = 2,678,571 $$
$$ \frac{3,000,000}{1.2544} = 2,392,344 $$
$$ \frac{3,000,000}{1.4049} = 2,136,695 $$
$$ \frac{3,000,000}{1.5735} = 1,907,603 $$
Sum:
$$ 2,678,571 + 2,392,344 + 2,136,695 + 1,907,603 = 9,115,213 $$
$$ NPV = 9,115,213 - 10,000,000 = -884,787 $$
Answer: NPV = -884,787 Ksh (project not financially viable)
Example 3: A school construction project costs Ksh 5,000,000 with expected cash inflows of Ksh 1,500,000, Ksh 2,000,000, and Ksh 2,500,000 over 3 years. Discount rate is 8%. Calculate NPV.
Given:
\(C_0 = 5,000,000\, Ksh\)
\(C_1 = 1,500,000\, Ksh\)
\(C_2 = 2,000,000\, Ksh\)
\(C_3 = 2,500,000\, Ksh\)
\(r = 0.08\)
\(n = 3\)
$$ NPV = \frac{1,500,000}{1.08} + \frac{2,000,000}{1.1664} + \frac{2,500,000}{1.2597} - 5,000,000 $$
$$ = 1,388,889 + 1,715,686 + 1,984,127 - 5,000,000 $$
$$ = 5,088,702 - 5,000,000 $$
Answer: NPV = 88,702 Ksh
Example 4: A cooperative plans a building with initial cost Ksh 3,000,000 and expected cash inflows of Ksh 1,200,000 per year for 3 years. Discount rate is 15%. Find NPV.
Given:
\(C_0 = 3,000,000\, Ksh\)
\(C_t = 1,200,000\, Ksh\) for \(t=1\) to 3
\(r = 0.15\)
\(n = 3\)
Calculate each term:
$$ \frac{1,200,000}{1.15} = 1,043,478 $$
$$ \frac{1,200,000}{1.3225} = 907,029 $$
$$ \frac{1,200,000}{1.5209} = 789,101 $$
Sum:
$$ 1,043,478 + 907,029 + 789,101 = 2,739,608 $$
$$ NPV = 2,739,608 - 3,000,000 = -260,392 $$
Answer: NPV = -260,392 Ksh
Example 5: A bank building project has an initial investment of Ksh 7,000,000. Expected cash inflows are Ksh 2,500,000, Ksh 3,000,000, and Ksh 3,500,000 over 3 years. Discount rate is 10%. Calculate NPV.
Given:
\(C_0 = 7,000,000\, Ksh\)
\(C_1 = 2,500,000\, Ksh\)
\(C_2 = 3,000,000\, Ksh\)
\(C_3 = 3,500,000\, Ksh\)
\(r = 0.10\)
\(n = 3\)
Calculate each term:
$$ \frac{2,500,000}{1.10} = 2,272,727 $$
$$ \frac{3,000,000}{1.21} = 2,479,339 $$
$$ \frac{3,500,000}{1.331} = 2,628,865 $$
Sum:
$$ 2,272,727 + 2,479,339 + 2,628,865 = 7,380,931 $$
$$ NPV = 7,380,931 - 7,000,000 = 380,931 $$
Answer: NPV = 380,931 Ksh
The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. It indicates the profitability of a project and helps compare investment options in building works.
The IRR satisfies:
$$ 0 = \sum_{t=1}^{n} \frac{C_t}{(1 + IRR)^t} - C_0 $$
Calculating IRR often requires trial and error or interpolation between discount rates.
Example 1: A building project has an initial cost of Ksh 1,000,000. Cash inflows are Ksh 400,000 per year for 3 years. Find IRR.
Given:
\(C_0 = 1,000,000\, Ksh\)
\(C_t = 400,000\, Ksh\) for \(t=1\) to 3
Try \(r=10\%\):$$ NPV = \sum \frac{400,000}{(1+0.10)^t} - 1,000,000 = ? $$
Calculate NPV at 10%:
$$ \frac{400,000}{1.10} = 363,636 $$
$$ \frac{400,000}{1.21} = 330,579 $$
$$ \frac{400,000}{1.331} = 300,526 $$
Sum:
$$ 363,636 + 330,579 + 300,526 = 994,741 $$
$$ NPV = 994,741 - 1,000,000 = -5,259 $$
Negative NPV at 10%.
Try \(r=9\%\):
$$ \frac{400,000}{1.09} = 366,972 $$
$$ \frac{400,000}{1.1881} = 336,556 $$
$$ \frac{400,000}{1.2950} = 308,858 $$
Sum:
$$ 366,972 + 336,556 + 308,858 = 1,012,386 $$
$$ NPV = 1,012,386 - 1,000,000 = 12,386 $$
Positive NPV at 9%.
Interpolation:
$$ IRR = 9\% + \frac{12,386}{12,386 + 5,259} \times (10\% - 9\%) $$
$$ = 9\% + \frac{12,386}{17,645} \times 1\% $$
$$ = 9\% + 0.702\% $$
$$ = 9.7\% $$
Answer: IRR ≈ 9.7%
Example 2: A cooperative invests Ksh 500,000 with returns of Ksh 200,000 annually for 3 years. Find IRR.
Calculate NPV at 12%:
$$ \frac{200,000}{1.12} = 178,571 $$
$$ \frac{200,000}{1.2544} = 159,444 $$
$$ \frac{200,000}{1.4049} = 142,306 $$
Sum:
$$ 178,571 + 159,444 + 142,306 = 480,321 $$
$$ NPV = 480,321 - 500,000 = -19,679 $$
Negative NPV at 12%.
At 10%:
$$ \frac{200,000}{1.10} = 181,818 $$
$$ \frac{200,000}{1.21} = 165,289 $$
$$ \frac{200,000}{1.331} = 150,263 $$
Sum:
$$ 181,818 + 165,289 + 150,263 = 497,370 $$
$$ NPV = 497,370 - 500,000 = -2,630 $$
Still negative but closer.
At 8%:
$$ \frac{200,000}{1.08} = 185,185 $$
$$ \frac{200,000}{1.1664} = 171,494 $$
$$ \frac{200,000}{1.2597} = 158,695 $$
Sum:
$$ 185,185 + 171,494 + 158,695 = 515,374 $$
$$ NPV = 515,374 - 500,000 = 15,374 $$
Positive NPV at 8%.
Interpolation:
$$ IRR = 8\% + \frac{15,374}{15,374 + 2,630} \times (10\% - 8\%) $$
$$ = 8\% + \frac{15,374}{18,004} \times 2\% $$
$$ = 8\% + 1.71\% $$
$$ = 9.71\% $$
Answer: IRR ≈ 9.7%
Example 3: A hotel project costs Ksh 4,000,000 and returns Ksh 1,500,000 annually for 4 years. Find IRR.
At 15%:
$$ \frac{1,500,000}{1.15} = 1,304,348 $$
$$ \frac{1,500,000}{1.3225} = 1,134,786 $$
$$ \frac{1,500,000}{1.5209} = 986,754 $$
$$ \frac{1,500,000}{1.749} = 857,338 $$
Sum:
$$ 1,304,348 + 1,134,786 + 986,754 + 857,338 = 4,283,226 $$
$$ NPV = 4,283,226 - 4,000,000 = 283,226 $$
Positive NPV at 15%.
At 20%:
$$ \frac{1,500,000}{1.20} = 1,250,000 $$
$$ \frac{1,500,000}{1.44} = 1,041,667 $$
$$ \frac{1,500,000}{1.728} = 868,056 $$
$$ \frac{1,500,000}{2.074} = 722,589 $$
Sum:
$$ 1,250,000 + 1,041,667 + 868,056 + 722,589 = 3,882,312 $$
$$ NPV = 3,882,312 - 4,000,000 = -117,688 $$
Negative NPV at 20%.
Interpolation:
$$ IRR = 15\% + \frac{283,226}{283,226 + 117,688} \times (20\% - 15\%) $$
$$ = 15\% + \frac{283,226}{400,914} \times 5\% $$
$$ = 15\% + 3.53\% $$
$$ = 18.53\% $$
Answer: IRR ≈ 18.5%
Example 4: A bank building costs Ksh 6,000,000 with expected cash inflows of Ksh 2,000,000 for 4 years. Find IRR.
At 13%:
$$ \frac{2,000,000}{1.13} = 1,769,912 $$
$$ \frac{2,000,000}{1.2769} = 1,565,526 $$
$$ \frac{2,000,000}{1.4429} = 1,386,049 $$
$$ \frac{2,000,000}{1.629} = 1,228,925 $$
Sum:
$$ 1,769,912 + 1,565,526 + 1,386,049 + 1,228,925 = 5,950,412 $$
$$ NPV = 5,950,412 - 6,000,000 = -49,588 $$
Negative NPV at 13%.
At 12%:
$$ \frac{2,000,000}{1.12} = 1,785,714 $$
$$ \frac{2,000,000}{1.2544} = 1,594,481 $$
$$ \frac{2,000,000}{1.4049} = 1,423,624 $$
$$ \frac{2,000,000}{1.5735} = 1,271,709 $$
Sum:
$$ 1,785,714 + 1,594,481 + 1,423,624 + 1,271,709 = 6,075,528 $$
$$ NPV = 6,075,528 - 6,000,000 = 75,528 $$
Positive NPV at 12%.
Interpolation:
$$ IRR = 12\% + \frac{75,528}{75,528 + 49,588} \times (13\% - 12\%) $$
$$ = 12\% + \frac{75,528}{125,116} \times 1\% $$
$$ = 12\% + 0.60\% $$
$$ = 12.6\% $$
Answer: IRR ≈ 12.6%
Example 5: A cooperative invests Ksh 800,000 with returns of Ksh 300,000 annually for 3 years. Find IRR.
At 15%:
$$ \frac{300,000}{1.15} = 260,870 $$
$$ \frac{300,000}{1.3225} = 226,890 $$
$$ \frac{300,000}{1.5209} = 197,211 $$
Sum:
$$ 260,870 + 226,890 + 197,211 = 684,971 $$
$$ NPV = 684,971 - 800,000 = -115,029 $$
Negative NPV at 15%.
At 10%:
$$ \frac{300,000}{1.10} = 272,727 $$
$$ \frac{300,000}{1.21} = 247,934 $$
$$ \frac{300,000}{1.331} = 225,394 $$
Sum:
$$ 272,727 + 247,934 + 225,394 = 746,055 $$
$$ NPV = 746,055 - 800,000 = -53,945 $$
Still negative.
At 5%:
$$ \frac{300,000}{1.05} = 285,714 $$
$$ \frac{300,000}{1.1025} = 272,108 $$
$$ \frac{300,000}{1.1576} = 258,962 $$
Sum:
$$ 285,714 + 272,108 + 258,962 = 816,784 $$
$$ NPV = 816,784 - 800,000 = 16,784 $$
Positive NPV at 5%.
Interpolation between 5% and 10%:
$$ IRR = 5\% + \frac{16,784}{16,784 + 53,945} \times (10\% - 5\%) $$
$$ = 5\% + \frac{16,784}{70,729} \times 5\% $$
$$ = 5\% + 1.18\% $$
$$ = 6.18\% $$
Answer: IRR ≈ 6.2%
The payback period is the time required for the cumulative cash inflows to equal the initial investment. It measures the liquidity risk and recovery time of the project.
The formula for payback period when cash inflows are equal is:
$$ \text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} $$
For uneven cash inflows, cumulative sums are used.
Example 1: A building project costs Ksh 1,200,000 and returns Ksh 400,000 annually. Find the payback period.
Given:
Initial investment = 1,200,000 Ksh
Annual cash inflow = 400,000 Ksh
$$ \text{Payback Period} = \frac{1,200,000}{400,000} = 3\, \text{years} $$
Answer: Payback period = 3 years
Example 2: A cooperative building costs Ksh 850,000. Expected cash inflows are Ksh 300,000 in year 1, Ksh 400,000 in year 2, and Ksh 300,000 in year 3. Find the payback period.
Calculate cumulative cash inflows:
Year 1: 300,000
Year 2: 300,000 + 400,000 = 700,000
Year 3: 700,000 + 300,000 = 1,000,000
Initial investment = 850,000
The payback occurs between year 2 and 3.
Amount to recover after year 2:
$$ 850,000 - 700,000 = 150,000 $$
In year 3, cash inflow = 300,000
Fraction of year 3 needed:
$$ \frac{150,000}{300,000} = 0.5\, \text{years} $$
Total payback period:
$$ 2 + 0.5 = 2.5\, \text{years} $$
Answer: Payback period = 2.5 years
Example 3: A hospital project costs Ksh 3,000,000. Cash inflows are Ksh 1,000,000, Ksh 1,200,000, and Ksh 1,500,000 over 3 years. Calculate payback period.
Cumulative inflows:
Year 1: 1,000,000
Year 2: 2,200,000
Year 3: 3,700,000
Investment = 3,000,000
Payback between year 2 and 3.
Amount left after year 2:
$$ 3,000,000 - 2,200,000 = 800,000 $$
Year 3 inflow = 1,500,000
Fraction of year 3:
$$ \frac{800,000}{1,500,000} = 0.533\, \text{years} $$
Total payback:
$$ 2 + 0.533 = 2.53\, \text{years} $$
Answer: Payback period = 2.53 years
Example 4: A retail building costs Ksh 1,500,000. Cash inflows are Ksh 500,000 annually. Calculate payback period.
$$ \text{Payback Period} = \frac{1,500,000}{500,000} = 3\, \text{years} $$
Answer: Payback period = 3 years
Example 5: A bank project costs Ksh 5,000,000. Cash inflows are Ksh 1,200,000 in year 1, Ksh 1,300,000 in year 2, Ksh 1,500,000 in year 3, and Ksh 1,800,000 in year 4. Find payback period.
Cumulative inflows:
Year 1: 1,200,000
Year 2: 2,500,000
Year 3: 4,000,000
Year 4: 5,800,000
Investment = 5,000,000
Payback between year 3 and 4.
Amount left after year 3:
$$ 5,000,000 - 4,000,000 = 1,000,000 $$
Year 4 inflow = 1,800,000
Fraction of year 4:
$$ \frac{1,000,000}{1,800,000} = 0.556\, \text{years} $$
Total payback:
$$ 3 + 0.556 = 3.56\, \text{years} $$
Answer: Payback period = 3.56 years
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Create a free accountThis chapter focused on preparing project appraisals by first identifying key appraisal items critical for evaluating building works, such as costs, benefits, risks, and timelines. It then explained how to assess these appraisal items through quantitative and qualitative methods, ensuring accurate measurement and realistic estimation of project parameters. The chapter emphasized the importance of thorough data collection and analysis to support decision-making. Finally, it covered the preparation of appraisal reports, detailing how to present findings clearly and systematically to stakeholders. The reports must include comprehensive evaluations, justifications, and recommendations to guide project approval or modification. Throughout, the chapter highlighted the need for precision and clarity in documenting appraisal processes to enhance project planning and control.
Calculate the total cost of a building project where the estimated quantities are: 500 bags of cement at Ksh 700 per bag, 10,000 bricks at Ksh 20 per brick, and 200 kg of steel at Ksh 150 per kg.
(3 marks)
A contractor estimates the labour cost for plastering walls of area 250 m² at Ksh 350 per m². Calculate the total labour cost.
(2 marks)
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