ECON 371 in Fall 2009
Suggested Answers to Assignment 2
Q1. You are considering making a movie. The movie is expected to cost $10 million
upfront and take a year to make. After that, it is expected to make $5 million
in the year it is released and $2 million for the following four years. Assume
that your cost of capital is 10%.
a). Calculate the payback period for this project. If you require a payback
period of four years, will you make the movie? What is(are) the major
aw(s) in this method?
b). Calculate the discounted payback period for this project. If you require a
discounted payback period of four years, will you make the movie? What
is(are) the major
aw(s) in this method?
c). Calculate the net present value of this project. Will you make the movie
based on the NPV of this project?
d). Write down the equation which you can use to solve for the IRR for this
project and then use Spreadsheet for ▯nd the IRR. Will you make the
movie based on the IRR of this project?
e). Calculate the pro▯tability index for this project.
An: a). The cumulative cash
ow is calculated in the following table:
ow Cumulative Cash Flow
0 -10 -10
1 5 -5
2 2 -3
3 2 -1
4 2 1
5 2 3
The payback period is 3 + = 3:5 years, which is less than the cuto▯
point of 4 years. Therefore, I will make the movie.
Payback has two drawbacks: 1) It ignores all the cash
ows after the cuto▯
point; 2) It ignores the time of money principle: it does not discount cash
b). The discounted and cumulative discounted cash
ow is calculated in the
1 Years Discounted Cash
ow Cumulative Discounted Cash Flow
0 -10 -10
1 4.5455 -5.4545
2 1.6529 -3.8017
3 1.5026 -2.2990
4 1.3660 -0.9330
5 1.2418 0.3088
The payback period is 4 +0:9330 = 4:7513 years, which is more than the
cuto▯ point of 4 years. Therefore, I will note make the movie.
Discounted payback method is better than the payback, but it still ignores
all the cash
ows after the cuto▯ point.
c). According to the table in b), NPV = 0:3088, which is positive. Therefore
I will make the movie.
▯10+ 5 + 2 + 2 + 2 + 2 = 0
1 + IRR (1 + IRR) 2 (1 + IRR) 3 (1 + IRR) 4 (1 + IRR)5
=) IRR = 11:4532%
PI = C = 10 = 0:0309
Q2. a). A project will cost $4,000 initially. It will generate $2,000 and $2,550 at
the end of year 1 and year 2. The cost of capital for next year is 5%. For
the year after, due to an expectation that the economy will experience a
higher growth, the cost of capital is expected to be 7%. Should you accept
the project using the NPV rule?
b). Victoria Management is trying to evaluate the following project:
Year Cash Flow
Write down the equation which you can use to solve for the IRR for this
project. Plot the NPV pro▯le for this project with the discount rate on
the horizontal axis and the NPV on the vertical axis (you may hand in a
printout for the graph, please use discount rate from 1% to 100%) and use
the IRR function in Excel to ▯nd the IRR.
2 An: a).
NPV = ▯4000 + + = 174:4548 > 0
1 + 5% (1 + 5%)(1 + 7%)
Therefore, accept the project.
▯400000 + 960000 + ▯572000 = 0
1 + IRR (1 + IRR) 2
IRR = 10%; IRR = 30%
See the last page for the NPV pro▯le.
Q3. The sales forecasts for Finance for their new product are given in the table
below. It has been estimated that every year expenses are equal to 60 percent
of that year’s sales forecasts. The annual working capital (WC) will be equal
to 20 percent of sales in the following year (i.e. today’s WC is equal to 20
percent of Year 1’s sales; Year 1’s WC is equal to 20 percent of Year 2’s sales;
...). Finance needs an initial investment of $800;000 in equipment which falls
into the asset class with a CCA rate of 30 percent. This equipment will be sold
after 6 years at $450;000 and Finance will still have other assets in this asset
class following the sale of the equipment. Finance has a marginal tax rate of
40 percent and its opportunity cost of capital is 15 percent. The half-year rule
a). What is the present value of cash
ows excluding CCA tax shields?
b). What is the present value of CCA tax shields?
c). Should Finance accept this new project?
An: a). CFO (excluding CCA tax shield) is calculated as the following:
3 Year 1 2 3 4 5 6
Revenue 1000000 1250000 1500000 950000 600000 300000
expenses 600000 750000 900000 570000 360000 180000