# Commerece 2FA3, Feb 2002, Tutorial 4 - DOC by 62ppN2T

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```									Com 2FA3                            Tutorial 7      Week of March 4, 2002

Question 1:

MGD Inc. is considering a capital budgeting proposal that would cost
\$200,000 to start. The project is forecast to generate annual cash flows of
\$25,000 per year for 12 years and have a salvage value of \$125,000 at that
time. MGD has a cost of capital of 9.75%. Evaluate this project using NPV,
IRR, PB, DPB, and PI.
k=  9.75%
The easiest method to calculate          T      CF      PV net PV
all of the required decision             0    -200 -200.00 -200.00
1      25   22.78 -177.22
criteria is to construct a table
2      25   20.76 -156.47
of the present value of each             3      25   18.91 -137.55
cash flow, since the discounted          4      25   17.23 -120.32
payback period is most readily           5      25   15.70 -104.62
6      25   14.31 -90.32
calculated in that manner.               7      25   13.03 -77.28
8      25   11.88 -65.40
The NPV, IRR and PI all accept           9      25   10.82 -54.58
the project. It is unclear if the       10      25    9.86 -44.72
PB or DPB criteria would accept         11      25    8.98 -35.74
12     150   49.12   13.38
the project since the cutoff               NPV =     13.38 > 0 accept
rate is arbitrary and not given.            IRR = 10.83% > cost of capital, accept
However, the payback period of                PI = 1.0669 > 1 accept
8 years is quite long, so it is              PB =        8 What cutoff value?
DPB =      11.7 What cutoff value?
likely that the payback criteria
would reject the project. The discounted payback being almost the
same as the life of the project would also be likely to reject the
project.

If multiple decision criteria are in use, the project will require further
study to assess its acceptability.
Com 2FA3                             Tutorial 7         Week of March 4, 2002

Question 2:

MFM Inc. is considering two mutually exclusive projects. Project A has a
startup cost of \$100,000 and is expected to generate cashflows of \$20,000
per year for ten years with no salvage value. Project B costs \$25,000 to start
and should generate \$6,000 per year with no salvage value. The cost of
capital for both projects is 11%.

 Find the NPV and IRR for each project.

 What decision should MFM's managers make?

 Why?

Copying the spreadsheet used in           k=      11.00%
A              B
question 1; you can calculate the            T         CF      PV     CF      PV
0       -100 -100.00    -25
NPV and IRR quite quickly.
-25.00
1         20   18.02      6     5.41
2         20   16.23      6     4.87
MFM should proceed with project              3         20   14.62      6     4.39
4         20   13.17      6     3.95
A because it will increase the               5         20   11.87      6     3.56
6         20   10.69      6
value of the company more than                                               3.21
7         20    9.63      6     2.89
if the company does project B                8         20    8.68      6     2.60
9         20    7.82      6     2.35
since the NPV is higher.                    10         20    7.04      6      2.11
NPV =               17.78           10.34
IRR =              15.1%           20.2%
This is an example of the scale
problem caused by the IRR when mutually exclusive projects are
considered. In this case although Project B's IRR is higher than the
IRR of project A, project A is on a larger scale than project B and
therefore has a better dollar value return.
Com 2FA3   Tutorial 7   Week of March 4, 2002
Com 2FA3                             Tutorial 7           Week of March 4, 2002

Question 3:

Quick Buck Inc. has a project that will cost \$450 to start. The project will
generate \$1,000 next year, but will cost \$555 to shut down during the
second year.

 Find the internal rates of return for this project.

 What decision should Quick Buck's management make if their cost of
capital is 7%?

 Describe the NPV profile.

This is an example of a project with non-conventional cash flows. There
are two sign changes over the life of the project. Therefore, there
can be more than two solutions that set the NPV equal to zero. With
only three total cash flows the NPV = 0 equation can be converted into
a quadratic equation by setting x = (1 + IRR) and multiplying both sides
by x2.                          \$1,000      555
0  \$450            
1  IRR 1  IRR2
0  450 x 2  1,000 x  555

 b  b 2  4ac
x
2a
 1,000  1,0002  4 450 555

2 450
x  1.0760 or x  1.1462
IRR  7.6% or IRR  14.62%
Com 2FA3                          Tutorial 7       Week of March 4, 2002

To figure out what decision should be made we should look at the NPV
profile. With a discount rate of 0% the NPV of the project is -\$5. At
an infinite discount rate, the NPV is -\$450. Since the NPV profile
crosses the x-axis twice, the NPV is positive if the company's discount
rate is between 7.60% and 14.62%. Given that Quick Buck's cost of
capital is 7%; the NPV will be negative and the project should be
rejected.

The NPV profile of the project is -\$5 at a discount rate of 0%. The
profile increases until it crosses the x-axis at 7.6%.       It reaches a
maximum and starts to decline, crossing the x-axis a second time at
14.62%. It continues to decline at a decreasing rate, approaching a
value of -\$450 as the discount rate approaches infinity.

NPV Profile

2

0

0%   5%   10%    15%      20%   25%      30%
-2

-4

-6

-8

-10

NPV

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