Assignment: Corporate Finance
Problem 1
1-year call option, S=100, E=87, rF=2% (annual)
1 step per year
How much should the call option worth?
Problem 2
If total return after tax on a certain project is 7.5%, and there are five financing choices available to investors:
(1) 7% interest rate and a 60% LTV ratio;
(2) 7.8% interest rate and a 70% LTV ratio;
(3) 8.5% interest rate and a 80% LTV ratio;
(4) 9.25% interest rate and a 90% LTV ratio;
(5) 9.75% interest rate and a 95% LTV ratio;
Suppose that there are three types of investors (A, B and C) whose tax rates are 15%, 25% and 35%, respectively.
Questions:
(1) Find out the financing choice for each type of investor and the corresponding after-tax return on equity.
(2) Which type of investor has the highest after-tax return on their equity?
Problem 3
You currently have $2,500,000. You want to invest it in the following three assets: 10-year US Treasury bond with coupon rate 3.5%, Blandy and Gourmange stocks, who have the following historical annual returns:
|
Year
|
Blandy
|
Gourmange
|
|
1
|
26.0%
|
47.0%
|
|
2
|
15.0%
|
-54.0%
|
|
3
|
-14.0%
|
15.0%
|
|
4
|
-15.0%
|
7.0%
|
|
5
|
2.0%
|
-28.0%
|
|
6
|
-10.0%
|
40.0%
|
|
7
|
22.0%
|
17.0%
|
|
8
|
30.0%
|
-23.0%
|
|
9
|
-32.0%
|
-4.0%
|
|
10
|
28.0%
|
75.0%
|
|
11
|
28.6%
|
51.7%
|
|
12
|
16.5%
|
-59.4%
|
|
13
|
-15.4%
|
16.5%
|
|
14
|
-16.5%
|
7.7%
|
|
15
|
2.2%
|
-30.8%
|
|
16
|
-11.0%
|
44.0%
|
|
17
|
62.2%
|
18.7%
|
|
18
|
33.0%
|
-25.3%
|
|
19
|
-35.2%
|
-4.4%
|
|
20
|
50.8%
|
82.5%
|
|
21
|
23.4%
|
42.3%
|
|
22
|
13.5%
|
-48.6%
|
|
23
|
-12.6%
|
13.5%
|
|
24
|
-13.5%
|
6.3%
|
|
25
|
1.8%
|
-25.2%
|
|
26
|
-9.0%
|
36.0%
|
|
27
|
18.8%
|
15.3%
|
|
28
|
27.0%
|
-20.7%
|
|
29
|
-28.8%
|
-3.6%
|
|
30
|
25.2%
|
67.5%
|
Your goal is to have the expected annual return of 7.2% with a minimum portfolio risk. How much money should you allocate to these three assets?
Problem 4
A real estate investor has the following information on an apartment building:
• Purchase Price is $1,125,000 with acquisition costs of $35,000
• 33,600 leasable square feet
• Initial rent of $1.5/sq. ft. per month and will increase at the beginning of each year for 5 percent per year. For example, the first year rent from month 1 to month 12 is $1.5/sq. ft., the 2nd year rent from month 1 to month 12 is $1.575 ($1.5*(1+5%)), and so on.
• Vacancy rate of 5% of gross rent per month.
• Operating expenses are 25% of effective gross income
• Three financing choices:
1. Mortgage with 75% LTV ratio, 20 years, monthly payments and 5% annual rate;
2. Mortgage with 80% LTV ratio, 20 years, monthly payments and 6% annual rate;
3. Mortgage with 85% LTV ratio, 20 years, monthly payments and 6.5% annual rate;
• Holding period is 3 years (36 months) and the capital improvement expenditure is assumed to be $20,000 at the end of the first year only (12 months).
• Expected increase in value is 50% in total when sold in year 3 (36 months), 5% selling expenses
• 75% depreciable with monthly depreciation.
• Investor's tax rate is 35%, and capital gain tax rate is 15%.
Questions:
1. Compute equity after-tax cash flows from month 1 to month 36 for each financing choice.
2. What is the equity after-tax annual return (internal rate of return) for each financing choice and which choice would you like to make?
Problem 5
Based on the Capital Asset Pricing Model (CAPM) and the diagram below, what is the return of the stock if its beta is 1.5 or 0.5?
Problem 6
Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 12%.
|
Year
|
Project A Cash flow
|
Project B Cash flow
|
|
0
|
-2500
|
-2500
|
|
1
|
900
|
50
|
|
2
|
800
|
600
|
|
3
|
1600
|
150
|
|
4
|
100
|
900
|
|
5
|
50
|
500
|
|
6
|
300
|
2500
|