The staff of Jefferson Medical Services has estimated the following net cash flo
ID: 2669922 • Letter: T
Question
The staff of Jefferson Medical Services has estimated the following net cash flows for a food services operation that it may in its out patient clinic:
Year Expected Net Cash Flow
0 ($100,000)
1 (30,000)
2 (30,000)
3 (30,000)
4 (30,000)
5 (30,000)
5(salvage value) (20,000)
The year 0 cash flow is the net investment outlay, while the final amount is the terminal cash flow. (the clinic is expected to move to a new bulding in five years.) All other flows represent net operating cash flows. Jefferson's corporate cost of capital is 10 percent.
a. What is project's IRR?
b. Assuming the project has average risk, what is its NPV?
c. Now assume that the operating cash flows in years 1 through 5 could be as low as $20,000 or as high as 40,000. Furthermore, the salvage value cash flow at the end of year 5 could be as low as $0 or as high as $30,000. What is the worst case and best case NPV?
Explanation / Answer
a.
cf(0) = -$100,000
cf(1) = 30,000
cf(2) = 30,000
cf(3) = 30,000
cf(4) = 30,000
cf(5) = 30,000+salvage value = 50,000
100000 = 30000*(1/(1+irr) + 1/(1+irr)^2+ 1/(1+irr)^3+ 1/(1+irr)^4)+ 50000*1/(1+irr)^5)
irr = 19.05%
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b.
NPV = -100000 + 30000*(1/1.1 + 1/1.1^2+ 1/1.1^3+ 1/1.1^4) + 50000*1/1.1^5
= $26,142.03
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c.
worst case:
cf(0) = -$100,000
cf(1) = 20,000
cf(2) = 20,000
cf(3) = 20,000
cf(4) = 20,000
cf(5) = 20,000+salvage value = 20,000
100000 = 20000*(1/(1+irr) + 1/(1+irr)^2+ 1/(1+irr)^3+ 1/(1+irr)^4)+ 20000*1/(1+irr)^5)
irr = 0
NPV = -100000 + 20000*(1/1.1 + 1/1.1^2+ 1/1.1^3+ 1/1.1^4) + 20000*1/1.1^5
= $24,184.26
best case:
cf(0) = -$100,000
cf(1) = 40,000
cf(2) = 40,000
cf(3) = 40,000
cf(4) = 40,000
cf(5) = 40,000+salvage value = 70,000
100000 = 40000*(1/(1+irr) + 1/(1+irr)^2+ 1/(1+irr)^3+ 1/(1+irr)^4)+ 70000*1/(1+irr)^5)
irr = 32.64%
NPV = -100000 + 40000*(1/1.1 + 1/1.1^2+ 1/1.1^3+ 1/1.1^4) + 70000*1/1.1^5
= $70,259.11
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