IRR, investment life, and cash inflows Oak Enterprises accepts projects earning

Question

IRR, investment life, and cash inflowsOak Enterprises accepts projects earning more than the firm's 11% cost of capital. Oak is currently considering a 13-year project that provides annual cash inflows of $20,000 and requires an initial investment of $179,300. (Note: All amounts are after taxes.)

a.Determine the IRR of this project. Is it acceptable?

b.Assuming that the cash inflows continue to be $20,000 per year, how many additional years would the flows have to continue to make the project acceptable (that is, to make it have an IRR of 11%)?

c.With the given life, initial investment, and cost of capital, what is the minimum annual cash inflow that the firm should accept?

Explanation / Answer

PV of annuity = P*[(1-(1+r)^(-n)) / r]

P - Periodic payment

r - rate per period

n - number of periods

PV of annuity = 20000*((1-(1+0.11)^(-13)) / 0.11) = 134997.41

NPV = initial investment + pv of annuity = -179300+134997.41 = 44302.59

a.

IRR is the rate at which NPV = 0

0 = -179300 + 20000*((1-(1+r)^(-13)) / r)

r = 0.05785 = 5.78%

Since the cost of capital is 11%, and IRR is only 5.78% the project is not acceptable.

b.

0 = -179300 + 20000*((1-(1+0.11)^(-n)) / 0.11)

n = 41.00 years

Additional years = 41-13 = 28 years

c.

0 = -179300 + x*((1-(1+0.11)^(-13)) / 0.11)

x = $26563.47

Cash inflow = $26563.47

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