What is the NPV of investing $2m per year in years 0 to 5 (at year-end)...

What is the NPV of investing $2m per year in years 0 to 5 (at year-end) to generate a $1m cash flow in year 6 growing at 2% per year forever if the cost of capital is 12%?

Solutions

Expert Solution

Cost of capital (i) = 12%

Investment amount $2 million per year in year 0 to 5

total number of payment (n) =6

paid at beginning. So it is annuity due.

present value of annnuity formula = P +(P*(1-(1/(1+I)^(n-1)))/i)

2 + (2*(1-(1/(1+12%)^(6-1)))/12%

=9.209552405 million

This is value at today as payment start today.

cash inflow start in year 6 = 1 million

growth rate thereafter (g) =2%

Value of cash inflows at year 5 = CF6/(i-g)

=1/(12%-2%)

=10

Value of cash inflow at year 5 or future vlaue =10

number of years gap (n) =5

present value = future value/(1+i)^n

=10/(1+12%)^5

=5.674268557

NPV = PV of cash inflows - PV of investment

=5.674268557-9.209552405

-3.535283848

NPV is -3.54 million. NPV is negative. So investment should not be made

jeff jeffy answered 2 years ago

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