Capital budgeting for a solar plant with a capital rationing limit
SunHarvest Ltd is evaluating a five-year project to install a solar rooftop system at its factory. The initial cost is R12,000,000, depreciated straight-line to zero over five years for tax purposes. The project is expected to reduce electricity costs by R4,000,000 in year 1, growing at 6% per year. Operating and maintenance costs will be R500,000 in year 1, also growing at 6% per year. The company's nominal after-tax cost of capital is 14%, and the corporate tax rate is 27%, paid in the same year. Working capital of R300,000 is required immediately and will be recovered at the end of year 5. The company has a capital rationing limit of R15,000,000. It is also considering Project B, which requires R5,000,000, has a three-year life, and an NPV of R1,200,000. Project A cannot be delayed; Project B can be delayed. Ignore depreciation recapture and inflation on working capital.
1. Calculate the NPV of Project A. Show the annual after-tax cash flows and the discounting. Recommend whether to invest.
Read the worked answer
Net operating savings before tax = (R4,000,000 − R500,000) × 1.06^(t−1) = R3,500,000 × 1.06^(t−1). Depreciation = R12,000,000/5 = R2,400,000 per year. Tax = 27% × (net operating savings − depreciation). After-tax cash flow = net operating savings − tax; add R300,000 working capital recovery in year 5.
| Year | Net operating savings | Depreciation | Taxable income | Tax at 27% | After-tax cash flow | DF at 14% | PV |
|---|---|---|---|---|---|---|---|
| 1 | 3,500,000 | 2,400,000 | 1,100,000 | 297,000 | 3,203,000 | 0.877193 | 2,809,649 |
| 2 | 3,710,000 | 2,400,000 | 1,310,000 | 353,700 | 3,356,300 | 0.769468 | 2,582,566 |
| 3 | 3,932,600 | 2,400,000 | 1,532,600 | 413,802 | 3,518,798 | 0.674972 | 2,375,089 |
| 4 | 4,168,556 | 2,400,000 | 1,768,556 | 477,510 | 3,691,046 | 0.592080 | 2,185,394 |
| 5 | 4,418,669 | 2,400,000 | 2,018,669 | 545,041 | 3,873,628 | 0.519369 | 2,011,? |
Correcting the year 5 PV: after-tax cash flow is R3,873,629 plus R300,000 recovery = R4,173,629; PV = R4,173,629 × 0.519369 = R2,167,643. Total PV of inflows = R12,120,341. Initial outlay = R12,000,000 + R300,000 = R12,300,000. NPV = R12,120,341 − R12,300,000 = −R179,659.
Recommendation: reject Project A because its NPV is negative. Under capital rationing, Project A would consume R12.3m of the R15m limit and leave only R2.7m, which is insufficient for Project B. Project B has a positive NPV of R1.2m and should be funded. Accepting A would destroy value and block B.
2. Calculate the equivalent annual annuity of Projects A and B and explain which is preferable if both are repeatable and capital is not rationed.
Read the worked answer
Equivalent annual annuity (EAA) converts an NPV into a level annual amount over the project's life, allowing projects with different lives to be compared.
Project A: annuity factor at 14% for 5 years = (1 − 1/1.14^5)/0.14 = (1 − 0.519369)/0.14 = 3.43308. EAA = −R179,659/3.43308 = −R52,336 per year.
Project B: annuity factor at 14% for 3 years = (1 − 1/1.14^3)/0.14 = (1 − 0.674972)/0.14 = 2.32163. EAA = R1,200,000/2.32163 = R516,880 per year.
Project B is preferable. Its EAA is positive and much higher than Project A's negative EAA. If capital is not rationed and both projects can be repeated, the company should invest in B and reject A. If capital is rationed, the profitability index also favours B: A = R12,120,341/R12,300,000 = 0.985; B = (R5,000,000 + R1,200,000)/R5,000,000 = 1.24. Both methods give the same ranking here because A has a negative NPV.
3. Identify the key assumptions and perform a sensitivity analysis on the year-1 electricity savings. Advise management on how to proceed.
Read the worked answer
Key assumptions include the 6% annual growth in savings and costs, the 14% nominal after-tax discount rate, the 27% tax rate, straight-line depreciation to zero, no residual value, full recovery of working capital, and the reliability of the R4,000,000 year-1 savings. The project is close to break-even, so small changes matter.
Sensitivity on year-1 savings. A 1% increase in the year-1 net operating savings is R35,000. After tax, that is R35,000 × 0.73 = R25,550 in year 1, growing at 6%. The present value of a growing annuity of R25,550 for 5 years at 14% with 6% growth is R25,550 × [1 − (1.06/1.14)^5]/(0.14 − 0.06) = R25,550 × 3.8103 = R97,353. To cover the negative NPV of R179,659, savings must increase by R179,659/R97,353 = 1.85%. A 2% increase in year-1 savings makes the NPV positive.
Management should not rely on a 2% improvement unless it is contractual or highly probable. It should negotiate a performance guarantee from the supplier, obtain an independent energy audit, and consider non-financial benefits such as carbon tax savings, energy security, and reputation. If those benefits are real and quantifiable, they should be included in the cash flows. On the current numbers, reject Project A and fund Project B.