Question

The owner of a number of gas stations is considering installing coffee machines in his gas stations. It will cost

$250,000

to install the coffee​ machines, and they are expected to boost cash flows by

$116,071

per year for their​ five-year working life. What must the cost of capital be if this investment has a profitability index of​ 1?

Answer 1

Questions ask for Cost of capital. In this question capital is IRR Internal rate of return which mean the rate where PV of cash inflows equate with Initial Investment.

Profitability index given in the question = 1

Profitability index is Present value of Cash inflows / Initial investment that means both are equal. So calculate IRR where both will be equal.

We will go with Trial and error method and then Interpolation. In trial and error method you need to take guess for rate calculate PV of cash inflows and keep on doin till you get 2 rates where 1 PV is lower than 250000 and 1 higher than it.

Calculate the PV @35%

PV= Annual savings x cumulative discounting factor @35% for 5 years.

[ For pv factor refer the tables or calculate as (100/135) + (100/135)²...........(100/135)⁵]

PV = 116071 x 2.219961412

PV = 257673.14

We get PV 257673.14 which is slightly higher than 250000. So now try higher rate to reduce NPV

Pv @ 37%

PV = 116071 x 2.142693138 [ Factor = (100/137)+........(100/137)⁵ ]

PV = 248704.54

We have 2 rates and now we eill go with interpolation

35 + [(257673.14 - 250000) / ( 257673.14 - 248704.54)] * 2

= 35 + 0.85555605 * 2

= 36.71% approx