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### Question

**Question 1: **

- Assume that you will deposit $4000 at the end of each of the next three years in a St. George bank account paying 8% interest. You currently have $7000 in the account. How much will you have in three years? In four years?
- You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15% return, what is the most you would pay for this investment?
- A bond has an 8% coupon, paid semi-annually. The face value is $100, and the bond matures in 6 years. If the bond currently sells for $91.137, what is the yield to maturity? What is the effective annual yield?

**Question 2: **

We have two investment projects A&B. Both projects cost $250, and we require a 15% return of the two investments.

Year A B

1 $100 $100

2 $100 $200

3 $100 0

4 $100 0

- Based on the payback period rule, which project would you pick? Explain.
- Based on the NPV rule, which project would you pick? Explain.
- Do a) and b) give you the same conclusion? If not, why? Please elaborate.
- What other methods can you use to evaluate proposed investments? Please explain.

**Question 3: **

The ABC Company has a WACC of 20%. Its cost of debt is 12%, which is equal to the risk-free rate of interest. If ABC's debt to equity ratio is 2, what is the cost of equity capital? ABC's equity beta is 1.5.

- What are the M&M propositions I, II and III, please use graphs/charts and words to explain.
- Based on the M&M proposition II, what is the beta of the entire firm?

### Solution

**Question 1 **

- Assume that you will deposit $4000 at the end of each of the next three years in a St. George bank account paying 8% interest. You currently have $7000 in the account. How much will you have in three years? In four years?

Balance after three years: 7000*1.08^3+4000*1.08^2+4000*1.08+4000=21803.58

Balance after 4 years: 21803.58*1.08^4=29663.53

Therefore, the calculation above is based on the time value of money, which describes the money which will be available to an individual for the present time and what is going to be the state of the same lump sum in the future. The formula which is being used as compounding period, first it calculates the lump sum that will be available at the end of three years and then for four years. It shows that the TVM is not depended only on the interest rate and the time value but also the number of times the compounding calculations can be compounded on the yearly basis.

2. You are looking into an investment that will pay you $12,000 per year for the next 10 years. If you require a 15% return, what is the most you would pay for this investment?

Present value of Annuity

15,0000[1-(1+0.15)^-10/0.15]

=$75281.53

The calculation above, shows the current annuity which is the present annuity and it calculates the amount individual will have on present basis.

3. A bond has an 8% coupon, paid semi-annually. The face value is $100, and the bond matures in 6 years. If the bond currently sells for $91.137, what is the yield to maturity? What is the effective annual yield?

Coupon payment: (8%*100)/91.137=8.77%

91.137=100/2[1-(1+YTM/2)^-2(6)/2]+100

YTM= 10%

YTM, Yield to Maturity, helps in calculating the rate on return of a bond and how much the investor would earn if they had invested in the bond at the current market price. It aslo has represented the discount rate which also equates the discount value of the coupon in future for the current market price.

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