Question

Investiment opportuity as folows: Year 0, unknown cash flow, Year 1 = 200 cash flos,,Year 2 = 400 cash flow, Year 3 = -100 cash flow, year 4= 500 cash flow, Year 5 = 200 cash flow

a. If other investments with comparble risk are earning 12% then how mudh shoud you be willing to pay for this investment?

If you purchace it for 800 then what is the anual rate of retun on the investment?

Answer 1

a.       If comparable projects earns 12% then we should calculate projects initial cash flow keeping IRR or rate as 12%

CF0 = ?

CF0 = CF1 /1.12^1 + CF2/1.12^2 + CF3/1.12^3 + CF4/1.12^4 + CF5/1.12^5

CF0 = 200 /1.12^1 + 400/1.12^2 + (-100)/1.12^3 + 500/1.12^4 + 200/1.12^5

CF0 = 178.54 + 318.76 + (71.14) + 317.53 + 113.38

CF0 = 857.52

b.       For getting annual rate of return from different cash flows, we need to perform IRR, for performing IRR we need to work on trial and error. To keep this clean IRR rate is directly used.

CF0 = - 800 [Given]

-CF0/(1+r)^0 + CF1 /(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4 + CF5/(1+r)^5 = 0

We need to perform trial and error for getting r or rate here, we used first 13% then 14% and then interpolated both the trials to get the discounting rate 14.79% which can make our following equation equal to zero.

-CF0/(1+14.79%)^0 + CF1 /(1+14.79%)^1 + CF2/(1+14.79%)^2 + CF3/(1+14.79%)^3 + CF4/(1+14.79%)^4 + CF5/(1+14.79%)^5 = 0

-800 + 174.2312048 + 303.5651273 - 66.11314733 + 287.9743328 + 100.3482299 = 0

The sum is near to zero hence our annual rate of return = 14.79%

(We can fix rate or r as 13% and 14% to see the results of 36.16 and 15.64 respectively for clearer understanding)