1)What Is the Future Value of $3 Million Invested for Five Years in Bank Certificates Of

Seminar 2

Problem #1

An art collector has the opportunity to invest in paintings. The paintings cost $3 million and are expected to be worth $3,829 million in five years. He also has the opportunity to invest in 5-year bank certificates of deposit, which guarantee a return of 6% per year.

1)What is the future value of $3 million invested for five years in bank certificates of deposit?

2)Which has the highest return?

a. The paintings.

b. The bank CDS.

3)What is the rate of return for an investment in these paintings?

4)Assuming you would be satisfied with a 6% return from holding these paintings, what is the maximum you would be willing to pay for them today (again assuming they will be worth $3.829 million in 5 years)?

Answers

1.FV = PV (1+r)t = $3,000,000 (1.06)5 = $3,000,000 (1.3382) = $4,014,677

2.Paintings$3,000,000will be worth$3,829,000in 5 years

Bank CDs$3,000,000will be worth$4,014,677in 5 years

Bank CDs have a higher return.

3.FV = PV (1+r)t

$3,829,000 = $3,000,000 (1+r)5

(1+r)5 = $3,829,000 / $3,000,000 = 1.2763

(1+r) = (1.2763).2 = 1.05

r = .05 or 5%

4.PV = FV/(1+r)t = $3,829,000 / (1.06)5 = $3,829,000 (.74726) = $2,861,252

Problem 2

Investment A pays $100 per year for three years. Investment B pays $80 per year for four years. Which of these investments has the higher present value if the discount rate is

1. 10%?
2. 25%?

Answers:

PVA = C [ 1 - 1/(1+r)t ]/r

a) PVAA=$100 [ 1 - 1/(1.10)3 ]/ .10 = 100 (2.4868) = $248.68

PVAB =$80 [ 1 - 1/(1.10)4]/.10 = 80 (3.1699) = $253.59

b)PVAA=$100 [ 1 - 1/(1.25)3]/ .25 = 100 (2.30811) = $195.20

PVAB =$80 [ 1 - 1/(1.25)4]/ .25 = 80 (2.36160) = $188.93

Problem 3

Consider the following cash flows on two mutually exclusive projects that require an annual return of 15%.

Year / Project A / Project B
0 / -$600,000 / -$1,800,000
1 / 270,000 / 1,000,000
2 / 350,000 / 700,000
3 / 300,000 / 900,000

a)Based on the discounted payback period rule, which project should be chosen?

b)If your decision rule is to accept the project with a greater IRR, which project should you choose?

c)Since you are fully aware of the IRR rule’s scale problem, you calculate the incremental IRR. Based on your computations, which project should you choose?

d)To be prudent, you compute the NPV for both projects. Which project should you choose? Is it consistent with the incremental IRR rule?

Solution:

a) Project A

Year / Discounted CF / Cumulative CF
0 / -$600,000 / -$600 ,000
1 / 234,783 / -365,217
2 / 264,650 / -100,576
3 / 197,255

DPP for A = 2 + 100,576/197,255 = 2.51 years

Analogously one can compute DPP for B = 2.68 years.

Hence, project A should be chosen.

b) IRR of A solves -600,000 + 270,000/(1+r) + 350/(1+r)2 + 300/(1+r)3 = 0. We obtain IRR = 24.3%

Analogously, IRR of B = 21.46%.

Hence, project A should be chosen

c) Incremental cash flows

Year / B-A
0 / -$1,200,000
1 / 730,000
2 / 350,000
3 / 600,000

Doing similarly to b), we get incremental IRR = 19.92%. Since it is > 15%, project B should be chosen.

d) NPV of A = -600,000 + 270,000/1.15 + 350/1.152 + 300/1.153 = 96,687.76

NPV of B = 190,630.39 > 96,687.76.

Hence, project B should be chosen. The NPV rule is consistent with the incremental IRR rule.

Problem #4

U-Eat-M Pizza is evaluating a new line of no-fat pizzas. The company has paid $40,000 for a marketing study which indicates the new product would have sales of $650,000 per year for the next six years. Making no-fat pizza requires a specialized high temperature baking oven made in Chicago selling for $450,000 with shipping and handling expenses of $10,000. Installing the new oven will cost $40,000. This new oven will be depreciated according to ACRS as a five-year asset with no market value at the end of six years. Annual fixed costs are projected at $80,000 and variable costs are projected at 60% of sales. Net working capital requirements are $75,000 for the six-year life of the project; the outlay for working capital will be recovered at the end of six years. The tax rate is 34% and the firm requires a 16% return.

1. What is the amount of initial investment that can be depreciated?
   
2. Calculate the annual depreciation and the ending book value each year for the fixed assets. What is the book value at the end of two years?
   
3. Prepare pro forma income statements for the project for years 1 through 6 in order to determine EBIT, taxes and unlevered net income.
   
4. Compute the Free Cash Flow for years 1 through 6.

1. What is the initial outlay at time zero (remember all cash flows at time zero, not just the total cost of equipment)?
   
2. What is the net present value of this project?
   
3. What is the IRR of this project?
   
4. What is the payback for this project?
   
5. Should the $40,000 marketing study be included in the project analysis? Consider that the project could not have been evaluated without this study; however, you must pay for this study whether or not you proceed with the project.

Problem #4 Answers

1.Equipment Cost + Shipping + Installation=$450,000+$10,000+$40,000=$500,000

2.ACRS Ending

Yearpercentage Depreciationbook value

1 20.00% .2000x$500,000=$100,000$400,000

2 32.00% .3200x500,000=160,000240,000*

3 19.20% .1920x500,000=96,000144,000

4 11.52% .1152x500,000=57,60086,400

5 11.52% .1152x500,000=57,60028,800

6 5.76% .0576x500,000=28,8000

3.Year 1Year 2Year 3Year 4Year 5Year 6

Sales Revenue$650,000$650,000$650,000$650,000$650,000$650,000

-Variable Costs-390,000-390,000-390,000-390,000-390,000-390,000

-Fixed Costs-80,000-80,000-80,000-80,000-80,000-80,000

-Depreciation-100,000-160,000-96,000-57,600-57,600-28,800

EBIT80,00020,00084,000122,400122,400151,200

-Taxes-27,200-6,800-28,560-41,616-41,616-51,408

Net Income$52,800$13,200$55,400$80,784$80,784$99,792

4.Year 1Year 2Year 3Year 4Year 5Year 6

Net Income52,80013,20055,40080,78480,78499,792

+Depreciation100,000160,00096,00057,60057,60028,800

- Increases in NWC0000075000

- CapEx000000

Free Cash Flow$152,000$173,000$151,440$138,384$138,384$203,592

Comment: For year 6, recovery of net working capital results in a cash inflow of $75,000. Fixed assets are fully depreciated at the end of year 6 and have zero market value, so there are no consequences for cash flows from disposal of fixed assets at the end of the project’s life. Total inflow for year 6 is $203,592 = ($99,792 + $28,800+ $75,000).

5.Initial cash outflow is $575,000 = $500,000 + $75,000 (Installed cost + net WC).

6.PV = $152,800/1.16 + $173,200/1.162 + $151,440/1.163 + $138,384/1.164

+ $138,384/1.165 + $203,592/1.166 = $583,338.58

NPV = $583,338.58 - $575,000 = $8,338.58 so the new product line is an acceptable investment.

1. The IRR is 16.539%.

8.YrCash FlowsCumulative

0-575,000-575,000

1152,800-422,200

2173,200-249,000

3151,440-97,560Payback = 3 + 97,560/(138,384) =

4138,38440,8243.7 Years

5138,384179,208

6203,592382,800

9. The cost of the $40,000 marketing study is a sunk cost and is irrelevant.