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Chapter 7
Investment Decision Rules
Note:
All problems in this chapter are available in MyFinanceLab. An asterisk (*) indicates problems
with a higher level of difficulty.
1. Plan:
We can compute the NPV of the project using Eq. (7.2). The cash flows are an immediate
$8 million outflow followed by an annuity inflow of $5 million per year for 3 years and a discount
rate of 8%.
Execute:
a. NPV
3
51
8
1
$4.885 million.
0.08
(1.08)
⎛⎞
=− +
−
=
⎜⎟
⎝⎠
The NPV rule dictates that you should accept this contract.
b. The value of the firm will increase by $4.885 million.
Evaluate:
The NPV rule indicates that by making the investment, your factory will increase
the value of the firm today by $4.885 million, so you should undertake the project.
2. Plan:
We can compute the NPV of the project using Eq. (7.2). The cash flows are an immediate
$100 million outflow followed by an annuity inflow of $30 million and a discount rate of 8%.
We can compute the IRR using a financial calculator or spreadsheet or by setting the NPV equal
to zero and solving for r. After we find the IRR we can compute the maximum deviation
allowable in the cost of capital estimate to leave the decision unchanged by subtracting the cost
of capital from the IRR.
Execute:
Timeline:
0
1
2
3
4
–100
30
30
30
13
0
NPV
100
1.08
0.08
$247.22 million
=−
=
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Berk/DeMarzo/Harford •
Fundamentals of Corporate Finance
The IRR solves
13
0
100
0
24.16%.
1
r
rr
⎛⎞
−=⇒
=
⎜⎟
+
⎝⎠
So, the cost of capital can be underestimated by 16.16% without changing the decision.
Evaluate:
The NPV rule indicates that by making the investment, your factory will increase
the value of the firm today by $4.885 million, so you should undertake the project. The IRR is
the discount rate that sets the net present value of the cash flows equal to zero. The difference
between the cost of capital and the IRR tells us the amount of estimation error in the cost of
capital estimate that can exist without altering the original decision.
3. Plan:
We can compute the NPV of agreeing to write the book ignoring any royalty payments
using Eq. (7.2). The cash flows are an immediate $10 million outflow followed by an annuity
inflow of 8 million per year for 3 years and a discount rate of 10%. We can compute the NPV
of the book with the royalty payments by first computing the present value of the royalties at
year three. Once we compute the royalties at year 3 we can compute the present value of the
royalties today and add that number to the NPV of agreeing to write the book ignoring any
royalty payments.
Execute:
a. Timeline:
0
1
2
3
10
–8
–8
–8
3
81
NPV
10
1
0.1
(1.1)
$9.895 million
=−
−
b. Timeline:
0
1
2
3
4
5
6
10
–8
–8
–8
5
5(1 – 0.3) 5(1 – 03)
2
First calculate the PV of the royalties at year 3. The royalties are a declining perpetuity:
=
−−
=
=
5
5
PV
0.1
( 0.3)
5
0.4
12.5 million
Chapter 7 Investment Decision Rules
71
so the value today is
=
=
royalties
3
12.5
PV
(1.1)
9.391.
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This note was uploaded on 02/09/2010 for the course FINA 3001 taught by Professor Molly during the Spring '10 term at University of Minnesota Duluth.
 Spring '10
 molly
 Finance

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