Part 1-
Assume all cash flows are after tax.
1. Determine, using both the NPV longhand equation and Excel, the net present value for a project that costs $124,000 and would yield cash flows of $15,000 the 1st year, $18,000 the 2nd year, $22,000 the 3rd year, $25,000 the 4th year, $29,000 the 5th year, and $35,000 the 6th year. Your firm's cost of capital is 8.00%.
2. Determine the net present value for a project that costs $294,105 and is expected to yield cash flows of $28,000 per year for the 1st 5 years, $39,000 per year for the next 5 years, and $49,000 per year for the following 5 years. Your firm's cost of capital is 6.00%.
3. Determine the internal rate of return for a project that costs $46,300 and would yield cash flows of $5,000 the 1st year, $7,000 the 2nd year, $9,000 the 3rd year, $13,000 the 4th year, $14,000 the 5th year, and $18,000 the 6th year.
4. Determine the internal rate of return for a project that costs $180,532 and is expected to yield cash flows of $25,000 per year for the first five years, $33,000 per year for the next five years, and $46,000 per year for the following five years.
5. Your company has an opportunity to invest in a project that is expected to result in cash flows of $18,000 the 1st year, $20,000 the 2nd year, $23,000 the 3rd year, -$8,000 the 4th year, $30,000 the 5th year, $36,000 the 6th year, $39,000 the seventh year, and -$6,000 the eighth year. The project would cost the firm $142,000. If the firm's cost of capital is 12%, what is the modified internal rate of return for the project?
6. Your company has an opportunity to invest in a long-term, slow-growth project that is expected to result in cash flows of $4,000 the 1st year, $6,000 the 2nd year, $7,000 the 3rd year, -$3,000 the 4th year, $25,000 the 5th year, $30,000 the 6th year, and $50,000 the 7th year. The project would cost the firm $61,500. If the firm's cost of capital is 12%, what is the modified internal rate of return for the project?
7. You are considering an investment with the following cash flows. Your required return is 6%, you generally require a payback of 3 years and a discounted payback of 4 years. If your objective is to maximize your wealth, should you take this investment?
|
Year
|
0
|
1
|
2
|
3
|
4
|
5
|
|
Cash Flow
|
-$50,000
|
$20,000
|
$20,000
|
$20,000
|
$20,000
|
-$30,000
|
8. Determine the payback period (in years) for a project that costs $150,000 and would yield cash flows of $30,000 the 1st year, $60,000 the 2nd year, $15,000 the 3rd year, $40,000 the 4th year, $25,000 the 5th year, and $33,000 the 6th year.
Part 2-
9. You are an executive within the Investor Relations team for a firm (you are primarily concerned with maximizing shareholder wealth), and a project is up for discussion. You must vote whether to make the investment, with only cash flow and NPV data. In which of the following situations should the investment be accepted, rejected, or neither (not enough information to determine), in your opinion?
a. The NPV of the investment is exactly equal to zero
b. The NPV of the investment is positive
c. The NPV of the investment is negative
d. The sum of the cash inflows flows of the investment is greater than the sum of the cash outflows, regardless of when the cash flows occur
e. The project under consideration has unconventional cash flows
10. You are a startup company, and you are considering a new project with an initial investment and positive future cash flows. You feel that your discount rate will be 8% based in your current credit situation, but there is a possibility that it will be higher. How would the increase in the discount rate affect the internal rate of return and NPV of the project?
11. A capital project costs $300M and has expected cash flows of $75M for the 1st three years and $50M in each of the project's last three years. If the discount rate is 8%, what is the discounted payback period?
12. You own some manufacturing equipment that must be replaced. Two different suppliers present a purchase and installation plan for your consideration, Supplier A and Supplier B. Project A costs $500K and has cash flows of $400K in each of the next 2 years. Project B also costs $500K, and generates cash flows of $500K and $275K for the next 2 years, respectively. Supplier B says you should select their project because you can achieve a return on your investment in just 1 year.
a. What is the crossover rate?
b. What is the NPV at the cross-over rate?
c. Which project should be selected (and why) if the actual cost of capital is:
- Equal to the crossover rate?
- Less than the crossover rate?
- Greater than the crossover rate?
13. You are going to choose between two investments. Both cost $50,000, but investment A pays $25,000 a year for 3 years while investment B pays $20,000 a year for 4 years. If your required return is 12%, which should you choose?
14. You have a choice between 2 mutually exclusive investments. If you require a 15% return, which investment should you choose?
|
|
A
|
B
|
|
Year
|
Cash flow
|
Cash Flow
|
|
0
|
-$100,000
|
-$125,000
|
|
1
|
$20,000
|
$75,000
|
|
2
|
$40,000
|
$45,000
|
|
3
|
$80,000
|
$40,000
|
15. Your car died and you need to borrow $13,000 quickly to buy a used car to get to work. It's Saturday afternoon and the bank just closed, but you can get a signature loan from a local pawn shop if you promise to repay them $1200 every month over the next year.
a. From the pawn shop's point of view, what is the IRR of this transaction?
b. What is the EAR (Effective Annual Rate) of this transaction?
c. Suppose that the pawn shop's cost of funds is 5%, compounded monthly. From their point of view, what is the NPV of this deal?
16. Bill plans to open a service center. The equipment will cost $75,000. Bill expects the after-tax cash inflows to be $20,000 annually for 8 years, after which he plans to scrap the equipment and retire.
a. What is the project's regular payback period?
b. Assume the required return is 10%. What is the project's discounted payback period?
c. Assume the required return is 10%. What is the project's NPV?
d. Assume the required return is 20%. What is the project's IRR? Should it be accepted?
Part 3-
17. You have an opportunity to invest in a new startup franchised business. The investment fee is $50,000 for the franchise fee, plus another $130,000 in equipment costs, and $90,000 for operational expenses. You expect the monthly operational costs to total 50% of gross revenues; additionally, interest, taxes, depreciation, and amortization will cost you approximately 40% of the remaining amount. If each item is sold for $600, and the cost of capital is 8%, how many items need to be sold each year (assume a constant rate) in the first 3 years year in order to:
a. Break even?
b. Earn $67,500 profit (future value)?
c. What is the NPV of b?
d. At the rate of production found in part a, how many years before the NPV is greater than the initial investment amount?
e. If the rate of production increases by 20% year over year (after year 1) in part d, how many years before the NPV is greater than the initial investment amount?
18. You are considering the purchase of a Pub. The asking price is $250,000, of which and $172,000 is for the property and equipment. The pro forma that the current owners projected for the next 5 years is shown below. If the future discount rate could vary between 1.75% and 5%, at what rates would this be a good deal? (calculate the rate at .25% increments; ignore depreciation)
|
|
2015
|
2016
|
2017
|
2018
|
2019
|
|
|
|
|
|
|
|
|
|
Gross Sales
|
Cash Sales - Food
|
$ 108,719
|
$ 86,975
|
$ 86,975
|
$ 86,975
|
$ 108,719
|
|
|
Cash Sales - Beverages
|
112,856
|
124142
|
108003
|
112323
|
110077
|
|
|
Cash Sales - Misc.
|
44,315
|
48747
|
48113
|
57735
|
63509
|
|
|
Total Cash Available
|
$ 265,890
|
$ 259,863
|
$ 243,091
|
$ 257,034
|
$ 282,305
|
|
Expenses
|
|
|
|
|
|
|
|
Variable Expenses
|
|
|
|
|
|
|
COGS - Beverage
|
28214
|
31318
|
26307
|
27359
|
26812
|
|
COGS - Food
|
35877
|
43052
|
42493
|
50991
|
56090
|
|
Hourly Wages & Benefits
|
29758
|
37198
|
28476
|
39670
|
42012
|
|
Total Variable Expenses
|
$ 93,849
|
$ 111,568
|
$ 97,275
|
$ 118,020
|
$ 124,914
|
|
Fixed Expenses
|
|
|
|
|
|
|
Direct Operating Expenses
|
|
|
|
|
|
|
Management Salaries
|
26,731
|
21385
|
21385
|
21385
|
26,731
|
|
China, Silver, Glassware
|
264
|
212
|
212
|
212
|
264
|
|
Equipment Rental
|
2404
|
1923
|
1923
|
1923
|
2,404
|
|
Licenses & Permits
|
481
|
385
|
385
|
385
|
481
|
|
Linenes/Uniforms
|
721
|
577
|
577
|
577
|
721
|
|
Janitorial
|
4327
|
3462
|
3462
|
3462
|
4,327
|
|
Supplies
|
2476
|
1981
|
1981
|
1981
|
2,476
|
|
Misc. Direct Operating Expenses
|
962
|
769
|
769
|
769
|
962
|
|
Total Direct Operating Expenses
|
38,366
|
$ 30,694
|
$ 30,694
|
$ 30,694
|
$ 38,366
|
|
General and Admin Expenses
|
|
|
|
|
|
|
Music and Entertainment
|
7212
|
5769
|
5769
|
5769
|
7212
|
|
Advertising and Promotion
|
19231
|
15385
|
15385
|
15385
|
19231
|
|
Credit Card Commission
|
1329
|
1064
|
1064
|
1064
|
1329
|
|
Professional Fees
|
2163
|
1731
|
1731
|
1731
|
2163
|
|
Insurance
|
4087
|
3269
|
3269
|
3269
|
4087
|
|
Excise Taxes
|
18612
|
14890
|
14890
|
14890
|
18612
|
|
Misc.
|
2404
|
1923
|
1923
|
1923
|
2404
|
|
Total General and Admin Expenses
|
55038
|
44031
|
44031
|
44031
|
55038
|
|
Rent
|
20833
|
20833
|
20833
|
20833
|
20833
|
|
Repairs and Maintenance
|
625
|
625
|
625
|
625
|
625
|
|
Utilities
|
5000
|
5000
|
5000
|
5000
|
5000
|
|
Long-Term Loan Repayment
|
20758
|
20758
|
20758
|
20758
|
20758
|
|
Management Fee
|
5318
|
4254
|
4254
|
4254
|
5318
|
|
Total Fixed Expenses
|
$ 145,938
|
$ 126,195
|
$ 126,195
|
$ 126,195
|
$ 145,938
|
|
Taxes
|
1432
|
1432
|
1432
|
1432
|
1432
|
|
Total Cash Paid Out
|
$ 241,219
|
$ 239,195
|
$ 224,902
|
$ 245,647
|
$ 272,284
|
|
Cash Flow
|
$ 24,671
|
$ 20,668
|
$ 18,189
|
$ 11,386
|
$ 10,021
|
19. Your company is considering whether to insource or to purchase a part for your product. In order to produce the part yourself, you will need to purchase the raw materials for a cost of $800 per part. It takes 6 months to create 90 parts. The total cost to produce one part is $870.15, including labor. The cost to purchase one part is $915.67, and you have 60 days to pay the invoice upon receipt of the parts. What would you recommend the company do if the annual discount rate is 8%? What if it were 12%? (Assume 30 days/month.)