Advanced Investment Appraisal
Investment
Advanced Investment Appraisal
Syllabus tag: KASNEB CPA | Advanced Level | CA33 Advanced Financial Management | Topic 2 Advanced Investment Appraisal
Lesson objectives
By the end of this topic, you will be able to:
- Apply the Fisher relationship between real and money rates
- Treat inflation consistently in a discounted cash flow
- Incorporate taxation and capital allowances
- Compute an equivalent annual cost for assets of unequal lives
- Rank projects under capital rationing
Why this matters
CA22 discounted clean cash flows at a given rate. Real appraisals involve inflation, tax relief on capital spending, assets that last different lengths of time, and more good projects than money. Each of those is a distinct technique.
Inflation: the Fisher relationship
(1 + money rate) = (1 + real rate) × (1 + inflation rate)
A real rate of 8% with inflation of 6%:
Money rate = (1.08 × 1.06) − 1 = 14.48%
Note it is not 14%. Adding the two rates omits the product term, and the error grows with the rates involved — which matters in an economy with high inflation.
The consistency rule is what examiners test:
| Cash flows | Discount at |
|---|---|
| Money (inflated) | Money rate |
| Real (today's prices) | Real rate |
Either pairing gives the same NPV. Mixing them does not, and it is the commonest error in this topic.
Use money terms where different cash flows inflate at different rates — wages at 9%, materials at 5% — because a single real rate cannot then be applied. Use real terms where everything inflates together, since it is quicker.
Taxation and capital allowances
Two separate tax effects, and both belong in the cash flows:
- Tax on operating cash flows, at the corporation tax rate
- Tax saved by capital allowances, which is a cash inflow
An asset costs KES 30,000,000, is written down at 25% reducing balance, and is sold for KES 6,000,000 at the end of year 4. Tax is 30%.
| Year | Allowance | Working | Tax saved at 30% |
|---|---|---|---|
| 1 | 7,500,000 | 25% × 30,000,000 | 2,250,000 |
| 2 | 5,625,000 | 25% × 22,500,000 | 1,687,500 |
| 3 | 4,218,750 | 25% × 16,875,000 | 1,265,625 |
| 4 | 6,656,250 | balancing: 12,656,250 − 6,000,000 | 1,996,875 |
| 24,000,000 |
Check: total allowances of 24,000,000 equal cost less scrap proceeds — 30,000,000 − 6,000,000. If they do not, the working is wrong.
Timing. Where tax is paid one year in arrears, every tax figure moves one year later in the cash flow, which materially changes the NPV. An examiner will state the timing and expects it applied.
Assets of unequal lives
Comparing a machine lasting three years with one lasting five on total present value is meaningless — of course the longer asset costs more.
Equivalent annual cost = PV of costs / Annuity factor for the life
| Machine A | Machine B | |
|---|---|---|
| Initial cost | 18,000,000 | 26,000,000 |
| Running cost a year | 5,000,000 | 4,000,000 |
| Life | 3 years | 5 years |
| Annuity factor at 10% | 2.4869 | 3.7908 |
| PV of costs | 30,434,260 | 41,163,147 |
| Equivalent annual cost | 12,238,066 | 10,858,735 |
Machine B is cheaper at 10.86m a year against 12.24m, despite costing 11 million more to buy. Comparing the total present values would have chosen wrongly.
The method assumes each asset is replaced indefinitely on the same terms. Where the need is genuinely one-off, or technology is changing fast, that assumption fails and the comparison is less reliable.
:::checkpoint A finance director rejects Machine B because it costs KES 8 million more up front and the company is short of cash. Explain what the EAC comparison shows and what separate question the cash constraint raises. :::
Capital rationing
Hard rationing is imposed externally — lenders will advance no more. Soft rationing is imposed by management, perhaps to enforce discipline or because good managers are scarce.
Where projects are divisible, rank by profitability index — NPV per shilling invested — and take them in order until the funds run out, accepting a fraction of the last.
Where projects are indivisible, ranking fails. The correct method is to examine feasible combinations and take the set with the highest total NPV, which may exclude the highest-ranked project because it leaves too little for anything else.
That contrast is the examinable point: the profitability index is a ranking tool and works only where fractions can be taken.
Other adjustments
Lease versus buy. A financing decision, separate from whether to invest. Appraise the investment first at the cost of capital; then compare the two funding routes at the after-tax cost of borrowing, since both are essentially debt.
Asset replacement cycles. How often to replace a vehicle is an EAC problem across candidate cycles — replace every two years, three years, four — with the lowest EAC winning.
Working capital. An increase is a cash outflow when it occurs and is recovered at the end of the project. Candidates routinely include the outflow and forget the recovery.
:::checkpoint A project needs KES 4 million of working capital in year 0, rising to 5 million in year 2, and ends in year 5. Set out the working capital cash flows in each year from 0 to 5. :::