Icfai P.a. Ii

Appraisal Criteria II 1. Fisherian Rate of Return: It is that discount rate at which NPV of two project is equal. It is given by the point of intersection of the NPV graphs of the two projects, as shown below: 1 Fisherian Rate of Return NPV 2

Discount Rate

Fisherian rate may not always exist for two competing projects because NPV profiles may not intersect or may intersect more than once making interpretation different. Adjusted Net Present Value: It is the project’s net present value adjusted for side effects of the financing decision. Adjusted net present value is calculated in the following steps: i. First the base case NPV should be calculated. Base case NPV is the project’s NPV assuming that the project is all equity financed. ii. Then, the base case NPV should be adjusted to give effect to the financing decisions i.e. for issue expenses, tax shield on debt etc. Illustration: 1. Consider a project which requires an initial investment outlay of Rs. 30 lakh and generates cash inflow equal to Rs. 5 lakh per annum for 5 years. Debt capacity is Rs. 10 lakh carrying an interest of 14% p.a. The opportunity cost of equity is 16% and tax rate is 30%. Assume issue expenses of 5% of the gross proceeds of equity.

The debt is to be repaid in 5 equal annual installments.

Solution: Base case NPV = -30 + 5xPVIFA( 16%, 5) = -30 + 5 x 3.274 = -30 + 16.37 = -13.73 Issue expenses = Equity required x 0.05 = 1.05 lakh .95 PV of tax shield on debt Year Debt at the Interest Tax shield PV of tax beginning @ 14% @ 30% shield @ 14% 11 10 1.40 0.420 0.368 12 8 1.12 0.336 0.258 13 6 0.84 0.252 0.170 14 4 0.56 0.168 0.099 15 2 0.28 0.084 0.044 PV of tax shield on interest 0.939 Adjusted NPV = -13.73 – 1.05 + 0.939 = -13.741

2. In the above example, what should be the minimum post-tax cash flow from the project so that it is acceptable?

Solution: Adjusted cost of capital, the minimum acceptable rate of return and the minimum post-tax cash flow to make the project acceptable can be calculated as follows: The adjusted NPV should be zero to make it acceptable. So, the base case NPV = -(PV of tax shield – Issuing cost) = - ( 0.939 – 1.05) = + 0.111 Let X be the annual income from the project. So, +0.111 = -30 + X PVIFA(16%, 5) X = 30.111/3.274 = 9.197 For minimum adjusted cost of capital, 9.197 PVIFA(%,5) = 30(Initial investment) PVIFA(%,5) = 30/9.197= 3.2619 From the PVIFA table, looking in 5 years row, corresponding rate is approximately 15.5%

Analysis of Simple, Non-simple, Pure and Mixed Investment: Simple investment – the cash outflows are followed by cash inflows. Non-simple investment- cash outflow occur more than once. Pure investment – the uncovered investment balance is either negative or zero throughout the life of the project and zero at the end of the project. Mixed investment – which is not pure investment. Illustration: A project has the following cash flow stream associated with it: Year Cash flow 0 -4,000 1 1,500 2 800 3 750 4 -800 5 3,523 Calculate a. The uncovered investment balances over the project life b. What type of investment is it?

Solution: The IRR of the project is the value of ‘r’ for which -4,000 + 1500 + 800 + 750 – 800 + 3,523 = 0 (1+r) (1+r)² (1+r)³ (1+r) (1+r)5 IRR r = 12% by trial and error method. Uncovered Investment Balances 4

Year

Uncovered investment at the beginning ( Ft - 1)

Interest for the year ( 1+r)

Cash flow at the end of the year CFt

Uncovered investment balance at the end of the year Ft-1 +( 1+ r) - CFt

1

-4000.0

480

1500

-2980.0

2

-2980

-357

800

-2537.0

3

-2537.6

-304.5

750

-2092.1

4

-2092.1

-251.1

-800

-3143.2

5

-3143.2

-377.2

3523

+2.6

The project is not a mixed investment as the uncovered investment balance is not greater than zero in any year of the project duration. The investment is non-simple pure investment. Interactions of Investment and financial decisions: We cannot separate the financing and investment decisions and the capital budgeting exercise can be extended to include the financing decisions. This can be done in two ways as follows: i) Adjust the discount rate or ii) the net present value to consider the side effects of financing the project such as the tax shield that can be claimed on the debt raised, subsidies allowed, issue expenses etc. The side effect of financing decision can be accounted for in the discount rate that has to be employed to the cash flows to calculate the NPV. Formulas developed by A. Modigliani and Miller B. Miles and Ezzel

According to M&M, r* = r( 1-TL) where, r = Opportunity cost of capital, if the project is totally equity financed T = Tax rate applicable to the firm L = Marginal contribution of the project to the firm’s debt capacity As per Miles and Ezzell formula, r* = r –LT x (1 +r) /1 + r(D) , rD = cost of debt. Illustration: Investment outlay = Rs. 30 lakh Cash inflow = Rs. 5 lakh per annum perpetually Debt capacity = Rs. 10 lakh with an interest of 14% The opportunity = 16% cost of capital or cost of equity Tax rate = 30% Calculate adjusted cost of capital using the above formulas

A. r* = 0.16( 1 –0.3 x 10/30) = 14.4% B. r* = ).16 – 10/30 x 0.14 x 0.3 x (1.16)/1.14 = 14.6% M&M formula is based on the assumption that the project generates a constant perpetual cash flow and supports permanent debt. The M&E formula considers the proportion of debt to be constant and does not follow any cash flow pattern. Economic Rate of return: In this method, the return actually earned on the uncovered balances is compared with the required rate of return (or the opportunity cost of capital). Steps: The uncovered investment balance at the beginning of the period under evaluation is compounded at the opportunity cost of capital. This is what the value of the investment should be, assuming there is no withdrawal of money from the project.

From the above, the cash flow from the project during year is reduced. The balance remaining will become the opening balance of unrecovered investment for investment for the succeeding year. The difference between the value of the investment at the beginning of the year and the end is called economic depreciation The economic income is calculated by reducing the economic depreciation from the cash inflow during the tear. The economic income expressed as a percentage of the investment balance at the beginning of the year is called “the economic rate of return”. Illustration: Projected cash flows of a company are as follows: Year 1 2 3 4 5 6 After 6 Cash flow 10 20 25 29.8 29.8 29.8 0 (Rs.lakh) Initial investment = Rs. 100 lakh, and the cost of capital =10%. Find the economic rate of return.

Year 1 2 3 4 5 6 Cash Flow 10.0 20.0 25.0 29.8 29.8 29.8 Present value*, @ 10% 100.0 100.0 90.0 74.0 51.6 27.0 start of the year Present value, end of 100.0 90.0 74.0 51.6 27.0 0.0 the year Change in value 0.0 -10.0 -16.0 -22.4 -24.6 -27.0 During the year Economic Income 10.0 10.0 9.0 7.4 5.2 2.8 Rate of Return 0.1 0.1 0.1 0.1 0.1 0.1 Economic Depreciation 0.0 10.0 16.0 22.4 24.6 27.0 As can be seen from the above table, the return expected by the investors from this project is 10 percentage, uniformly for all the years. * Ft = Ft –1 (1 + r) - C t