?IRR, investment? life, and cash inflows???Oak Enterprises accepts projects earning more than the? firm's 12?% cost of capital. Oak is currently considering a 12?-year project that provides annual cash inflows of ?$30,000 and requires an initial investment of ?$242,800. ? (?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 ?$30,000 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 12?%)?
c.??With the given? life, initial? investment, and cost of? capital, what is the minimum annual cash inflow that the firm should? accept?
Year | Cash Flows | PVF@5% | PV | PVF@10% | PV | |||||||
0 | -242800 | 1 | -242800 | 1 | -242800 | |||||||
1 | 30000 | 0.952381 | 28571.43 | 0.9090909 | 27272.73 | |||||||
2 | 30000 | 0.907029 | 27210.88 | 0.8264463 | 24793.39 | |||||||
3 | 30000 | 0.863838 | 25915.13 | 0.7513148 | 22539.44 | |||||||
4 | 30000 | 0.822702 | 24681.07 | 0.6830135 | 20490.4 | |||||||
5 | 30000 | 0.783526 | 23505.78 | 0.6209213 | 18627.64 | |||||||
6 | 30000 | 0.746215 | 22386.46 | 0.5644739 | 16934.22 | |||||||
7 | 30000 | 0.710681 | 21320.44 | 0.5131581 | 15394.74 | |||||||
8 | 30000 | 0.676839 | 20305.18 | 0.4665074 | 13995.22 | |||||||
9 | 30000 | 0.644609 | 19338.27 | 0.4240976 | 12722.93 | |||||||
10 | 30000 | 0.613913 | 18417.4 | 0.3855433 | 11566.3 | |||||||
11 | 30000 | 0.584679 | 17540.38 | 0.3504939 | 10514.82 | |||||||
12 | 30000 | 0.556837 | 16705.12 | 0.3186308 | 9558.925 | |||||||
NPV | 23097.55 | -38389.2 | ||||||||||
IRR | 5 + 23097.55/61486.79 * 5 | 6.878% | ||||||||||
Hence the Project is not acceptable as the IRR is less than the expected return we want the return of 12% but it provides only 6.878% | ||||||||||||
Answer (b) | ||||||||||||
The total number of years at which the project becomes acceptable with same cash flows are | ||||||||||||
30000 * PVAF(12% , n) | = | 242800 | ||||||||||
Therefore PVAF(12%,n) | = | 8.093333 | ||||||||||
Therefore n = 31 years (approx) | ||||||||||||
Answer ( c ) | ||||||||||||
The minimum Cash inflow a company can accept for the given? life, initial? investment, and cost of? capital to make the project acceptable | ||||||||||||
let the cash inflow be X | ||||||||||||
Therefore | ||||||||||||
X*PVAf(12%,12) | = | 242800 | ||||||||||
X * 6.1943 | = | 242800 | ||||||||||
Therefore X | = | 242800 / 6.1943 | ||||||||||
Minimum Cash inflow | = | 39197.33 | ||||||||||
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