Question

You just finished analyzing a capital investment that will produce equal annual cash flows of $25 million of over its 5-year life. The resulting NPV is $8 million and the IRR is 15.13%. You assumed a $30 million salvage value, $20 million above its adjusted tax basis, and a 35% marginal tax rate. What discount rate did you use to value this investment?

please show the answer step by step and do not use excel

Answer 1

SOLUTION:-

The discounting rate used in this investment is 12.091%

EXPLANATION:-

Step 1 calculation of initial investment

Using IRR and Annual cash-flows, salvage values, tax rate we can find the Initial Investment. IRR is the Rate at which the Present value of the Cash inflows will be equal to Initial Investment.
Computation of the present value of cashflow at IRR at 15.13% is as follows:-

Year	cash Flow($ in millions)	PV at 15.13%	Present Value
1	25	.8686	21.7146
2	25	.7544	18.8609
3	25	.6553	16.3823
4	25	.5692	14.2294
5	25	.4944	12.3594
6	23	.4944	11.3707
Total			94.9171

After tax salvage value in year 5 = 10M + (20M * 1- tax rate)

=10M + 13M

= 23M

Hence the initial Investment is $94.92 Million approx.

Step 2 calculation of discount rate

Using initial investment, NPV and cash flows we can calculate the discount rate

NPV = Total cash discounted flow - Initial Investment

total discounted cashflow = initial investment + NPV

= $94.92M + $8M

=$102.92M

Lets assume discount rate = D

by substituting values in the discount cash flow formula we get,

By solving the above equation D = 12.09%

Discount rate used = 12.09%