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 $4 million and the profitability index is 1.05. 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 steps, no excel.

Answer 1

Answer-

Given

Annual cash flows = $ 25 million
Number of years = 5
NPV = $ 4 million
Tax rate = 35 % = 0.35
Profitability index = 1.05
Profitability Index = NPV of all cash flows / Initial investment
1.05 = $ 4 / Initial investment

Initial investment = $ 4 / 1.05 = $  3.81

The after-tax cash flows for each year during the 5-year life is given by:

= Pretax cash flows x (1 - marginal tax rate)

= $ 25 million x (1 - 35%)

= $ 25 million x ( 1 - 0.35)

= $ 25 million x 0.65
= $ 16.25 million

The after-tax income earned at the end of the useful life is given by:

= Amount assumed above the adjusted tax basis x (1 - marginal tax rate)

= $ 20 million x (1 - 35%)

= $ 20 million x ( 1 - 0.35)
= $ 20 million x 0.65
= $ 13 million

The total cash flow at the end of the useful life 5 years is

= Adjusted tax basis value + after-tax income at the end of useful life + after-tax cash flow for the 5th year

= $10 million + $13 million + $16.25 million

= $ 39.25 million

NPV = - Initial investment + CF1 / ( 1+r)1 + CF2 / ( 1+r)2  ​​ + CF 3 / ( 1+r)3 +  CF4 / ( 1+r)4 ​​​​​​​+ CF 5 / ( 1+r)5

$ 4 m = - $ 3.81 m + $ 16.25 m / ( 1+r)1 + $ 16.25m / ( 1+r)2  ​​ + 16.25m  / ( 1+r)3 ​​​​​​​+ $ 16.25m  / ( 1+r)4 ​​​​​​​+ $ 39.25m  / ( 1+r)5

By solving the above equation with financial calculator we get the discount rate

0 = - $ 7.81 + $ 16.25 m / ( 1+r)1 + $ 16.25m / ( 1+r)2  ​​ + 16.25m  / ( 1+r)3 ​​​​​​​+ $ 16.25m  / ( 1+r)4 ​​​​​​​+ $ 39.25m  / ( 1+r)5

r = 209.5 %

Note - Some input is wrong the NPV and profitability index. The solution is as per the given data.