a. Consider a project that costs $100 today and yields $121 of benefits two year
ID: 2810000 • Letter: A
Question
a. Consider a project that costs $100 today and yields $121 of benefits two years from today, with no other benefits or costs. What is its internal rate of return? b. Consider a second project, which costs $1,000 today and yields $1,080 of benefits one year from today, with no other benefits or costs. What is its internal rate of return? c. Suppose that, for each project, the relevant discount rate is 5 percent. Is the first project worth doing? Is the second project worth doing? Please explain. d. Suppose that, due to legal restrictions, at most one of the projects can be done. Should either be done and, if so, which one? Please explain.
Explanation / Answer
a)
IRR of first project:
IRR is the rate of return that makes cash inflows eqaul to cash outflows
100 = 121 / ( 1 + r)2
Using trial and error method i.e, after trying various values for R let's tyr R as 10%
100 = 121 / ( 1 + 0.1)2
Therefore IRR for first project is 10%
b)
IRR of second project:
IRR is the rate of return that makes cash inflows eqaul to cash outflows
1000 = 1080 / ( 1 + r)1
Using trial and error method i.e, after trying various values for R let's tyr R as 8%
1000 = 1080 / ( 1 + 0.8)1
1000 = 1000
Therefore IRR for second project is 8%.
To determine if the projcet is worth doing, we find the NPV:
NPV = Present value of cash inflows - present value of cash outflows
c)
NPV for first project:
NPV = -100 + 121 / ( 1 + 0.05)2
NPV = 9.75
First project is worth doing as it has a positive NPV
NPV for second project:
NPV = -1000 + 1080 / ( 1 + 0.05)1
NPV = 28.57
Second project is worth doing as it has a positive NPV
d)
We should do the second project as it has the highest NPV. When projects are mutually exclusive as in this case, we always go with the project which has the highest NPV.
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