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# Risk and Return

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1) Bill Broodiest, star quarterback for the Spring Bay Smashers, would like to invest a small portion of his earnings in stocks of one of three firms.  His estimated dividends and the probabilities of their occurrence follow.
.1             \$ 1200
.3            800
.4            1000
.2             1200

B) Grasshopper tractor
.2        \$0
.4           700
.4           800
.2           900

C) Breathiest Electronics
.1             \$500
.2              700
.3               900
.2              1100
1               12000

a) Calculate the expected cash flow for each.
b) Calculate the coefficient of variation for each.
c) Rank the three from the least risky to the most risky

2) The Pan American Bottling Co. is considering the purchase of a new machine that would increase the speed of bottling and save money. The net cost of this machine is \$45,000. The annual cash flows have the following projections:
Year Cash Flow
1 . . . . . . . . . . \$15,000
2 . . . . . . . . . . 20,000
3 . . . . . . . . . . 25,000
4 . . . . . . . . . . 10,000
5 . . . . . . . . . . 5,000

a. If the cost of capital is 10 percent, what is the net present value of selecting a new machine?
b. What is the internal rate of return?
c. Should the project be accepted? Why?

3) Mr. Sam Golff desires to invest a portion of his assets in rental property. He has narrowed his choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present owners, Mr Golff has developed the following estimates of the cash flows for these properties.
Palmer heights Crenshaw Village
Yearly Aftertax Cash Inflow (in thousands) Probability Yearly Aftertax Cash Inflow (in thousands) Probability
\$10 0.1 \$15 0.2
15 0.2 20 0.3
30 0.4 30 0.4
45 0.2 40 0.1
50 0.1

1. Find the expected value of the cash flow from each apartment complex.
2. What is the coefficient of variation for each apartment complex?
3. Which apartment complex has more risk?

#### Solution Preview

Bill Broodiest, star quarterback for the Spring Bay Smashers, would like to invest a small portion of his earnings in stocks of one of three firms.  His estimated dividends and the probabilities of their occurrence follow.

.1             \$ 1200
.3            800
.4            1000
.2             1200

B) Grasshopper tractor
.2        \$0
.4           700
.4           800
.2           900

C) Breathiest Electronics
.1             \$500
.2              700
.3               900
.2              1100
1               12000

a) Calculate the expected cash flow for each.
b) Calculate the coefficient of variation for each.
c) Rank the three from the least risky to the most risky

A) Galaxy Communication
Cash flows Probability Cash flow x Probability Difference from mean, i.e.1000 Difference 2 Prob x Difference 2
\$1,200 0.10 \$120 200 40,000 4,000
=1200x0.1 =1200-1000 =200^2 =0.1x40000
\$800 0.30 \$240 -200 40,000 12,000
\$1,000 0.40 \$400 0 0 0
\$1,200 0.20 \$240 200 40,000 8,000

Total= 1.00 \$1,000 24,000

Expected cash flow= \$1,000.00
Variance= 24,000
Standard deviation=&#8730;Variance= \$154.92 =&#8730;24000
Coefficient of variation = SD/Mean= 0.1549 =154.92/1000.

B) Grasshopper tractor
Cash flows Probability Cash flow x Probability Difference from mean, i.e.630 Difference 2 Prob x Difference 2
\$0 0.20 \$0 -630 396,900 79,380
=0x0.2 =0-630 =-630^2 =0.2x396900
\$700 0.30 \$210 70 4,900 1,470
\$800 0.30 \$240 170 28,900 8,670
\$900 0.20 \$180 270 72,900 14,580

Total= 1.00 \$630 104,100

Expected cash ...

#### Solution Summary

Answers questions on Capital Budgeting (NPV, IRR) and evaluation of risk using coefficient of variation.

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