- Adjusted NPV
- Modified NPV and modified IRR
- Equity NPV/IRR & Project NPV/IRR
- Inflation under capital budgeting
- Comparison in case of unequal lives/Equivalent annual NPV
- Replacement decision
Adjusted NPV
Two-step NPV:
Step 1: 100%-equity finances, no issuing cost, asset b. Focus is on the inherent economic value of the project
Step 2: financing aspects of the project: issuing costs, capital grants or interest subsidies
APV= base case NPV – flotation cost +tax advantage of debt.
Where base case NPV= NPV of the project assuming that it is all equity financed.
Flotation case = cost incur to raise the money
Tax advantage of debt = PV of ITS discounted at interest rate on debt.
Technically, an APV valuation model looks pretty much the same as a standard DCF model. However, instead of WACC, cash flows would be discounted at the unlevered cost of equity, and tax shields at the cost of debt. APV and the standard DCF approaches should give the identical result if the capital structure remains stable.
A project involve initial investment Rs 1,00,000 to be financed equally by equity and 10% debt. The whole of the initial investment shall be in fixed assets. Straight line depreciation is allowed for tax purpose assuming 5- year working life and no terminal value. Project EBDIT are as below:
Year
1 2 3 4 5 EBDIT (Rs ’000)
40 45 45 40 35 Cost of an unlevered equity is 15% and tax rate is 40%. The loan is repaid in 5 equal annual installments. Determine APV for the project.
Modified NPV and modified IRR
The NPV method assumes that cash flows are reinvested at the firm’s discount rate while the IRR method assumes that cash flows are reinvested at the project’s IRR. However, it may be that neither of these assumptions are correct.
Modified NPV as follows:
- Compute the cash flow and cash outflow as usual
- Compute PV cash outgo by using cost of capital as discount rate
- Find the future cash flows at the given rate of investment for the remaining years. So if the project is for the 5 years, the cash flow generated in first year end shall be compounded for remaining 4 years. Similarly the cash inflow generated in second year end shall be compounded for 3 years and so on.
- Take the total of future cash values which may be termed as future value or terminal value.
- Find the PV of the cash inflow In the following manner:
- Modified NPV: PV of cash inflows- PV of cash outgoes
Modified IRR:
The cost of capital or discount rate at which modified NPV is Zero is know as Modified IRR.
You are trying to choose between the following projects, but the correct reinvestment rate for your company is 15%, whereas the firm’s discount rate is 12%. Calculate each project’s NPV, IRR, modified NPV and modified IRR and select the better project.
| Year | Project A | Project B |
| 0 | -10,000 | -10,000 |
| 1 | 8,000 | 1,000 |
| 2 | 4,000 | 4,000 |
| 3 | 1,000 | 10,000 |
Equity NPV/IRR & Project NPV/IRR
NPV or IRR from the point of view of equity shareholder is called Equity NPV or Equity & similarly NPV or IRR computed from the point of view of overall company or project is called project NPV or project IRR.
Equity Shares Capital Rs. 50 crores, loans at the rate of interest of 15% p.a. from financial institutions Rs. 150 crores. The Project after completion will be opened to traffic and a toll will be collected for a period of 15 years from the vehicles using the road. The company is also required to maintain the road during the above 15 years and after the completion of that period, it will be handed over to the Highway authorities at zero value. It is estimated that the toll revenue will be Rs. 50 crores per annum and the annual toll collection expenses including maintenance of the roads will amount to 5% of the project cost. The company considers to write off the total cost of the project in 15 years on a straight line basis. For Corporate Income-tax purposes the company is allowed to take depreciation @ 10% on WDV basis. The financial institutions are agreeable for the repayment of the loan in 15 equal annual installments – consisting of principal and interest.
Calculate Project IRR and Equity IRR. Ignore Corporate taxation.
Inflation and Capital Budgeting
Inflation erodes the purchasing power, money and hence investors requires compensation for inflation. Since a project generates CF over a no. of Years the inflation effects may be dominant. Hence inflation is an important component in Capital budgeting. The principal of inflation and Capital Budgeting states that nominal/real CFs should be discounted at nominal/real Kc. In case of inconsistency we can adjust either the CFs or Kc. However sometimes inflation rates for revenue and cost are separately given. In such a a case we can only adjust CFs and not Kc.
- Money cash flow=Real cash flow*(1+ inflation rate)
- (1+money dis rate)= (1+ real dis rate)*(1+inflation rate)
Inflation rate may be symmetrical( one rate) or asymmetrical (multiple rate). Symmetrical inflation means all items of revenue and cost have undergone same level of inflation. Asymmetrical inflation means some items have suffered inflation at the rate that are different from those of others.
Year 1 2 3 4 Rs 10,000 20,000 30,000 5,000
The company’s cost of capital, incorporating a requirement for growth in dividends to keep pace with cost inflation is 20%, and this is used for the purpose of investment appraisal. On the above basis the divisional manager involved has recommended rejection of the proposal. Having regard to your on forecast that the rate of inflation is likely to be 15% in year 1 and 10%, in each of the following years, you are asked to comment fully on his recommendation. (Discounting figures at 20% are 0.833, 0.694, 0.579 and 0.482 respectively for year 1 to year 4.) (ICWAI)
Comparison in case of unequal lives/ Equivalent annual NPV
In case of life disparity we use annual capital charge (ACC) or equivalent annual net present value concept for each project by applying the following formula
Company X is forced to choose between two machines A and B. The two machines are designed differently, but have identical capacity and do exactly the same job. Machine A costs Rs. 1,50,000 and will last for 3 years. It costs Rs. 40,000 per year to run. Machine B is an ‘economy’ model costing only Rs. 1,00,000, but will last only for 2 years, and costs Rs. 60,000 per year to run. These are real cash flows. The costs are forecasted in rupees of constant purchasing power. Ignore tax. Opportunity cost of capital is 10 per cent. Which machine company X should buy?
Replacement decision
Initial investment = cost of new machine – PT salvage value of old machine.
Operating flow = EBDIT (1-t) +DTS
EBDIT savings in operating cost and DTS = DTS on new machine – DTS on old machine.
Terminal flow = PTSV from new machine- PTSV from old machine.
Alternatively, the company can buy a new machine for Rs. 49,000 with an expected life of 10 years with no salvage value after providing depreciation on straight line basis. In this case, running and maintenance costs will reduce to Rs. 14,000 each year and are not expected to increase much in real term for a few years at least. S Engineering Company regard a normal return of 10% p.a. after tax as a minimum requirement on any new investment. Considering capital budgeting techniques, which alternative will you choose? Take corporate tax rate of 50% and assume that depreciation on straight line basis will be accepted for tax purposes also.
Given cumulative present value of Re. 1 p.a. at 10% for 5 years Rs. 3.791, 10 years Rs. 6.145.
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