Remember, you must show your calculations to receive credit. To show how you calculated an answer using the time value functions on your calculator, you may show this as the text does on page 258 on the bottom left. For example when solving for the FV, you may show this as:

**N** = 4

**I/Y** = 10

**PV** = -1,000

**PMT** = 0

Solve for (**CPT**)**FV** = $1,464.10

To solve these time value problems, you may use any of 3 methods. You may use the appendices at the back of the textbook (these are also provided in the Course Information tab in Blackboard), you may use the formulas in the text, or you may use the time value functions on your calculator. I strongly recommend that you use one method and check your work using another method (keeping in mind that the appendices have factors that are rounded off and your answers using the appendices will be slightly different than using the formulas or the calculator time value functions).

__Chapter 9 Problems__

- What is the present value of:
*a*. $80,000 in 10 years at 6 percent?*b*. $106,000 in 5 years at 10 percent?*c*. $250,000 in 15 years at 8 percent?

- If you invest $20,000 today, how much will you have:
*a*. In 5 years at 10 percent?*b*. In 10 years at 10 percent?*c*. In 20 years at 10 percent?*d*. In 20 years at 10 percent (compounded semiannually)?

- How much would you have to invest today to receive:
*a*. $120,000 in 6 years at 8 percent?*b*. $150,000 in 15 years at 8 percent?*c*. $15,000 each year for 5 years at 6 percent?*d*. $40,000 each year for 20 years at 6 percent?

- Bobbie Cohen will receive $ 250,000 in 30 years from a fund her parents have established to help her in her retirement years. Her friends are very jealous of her. If the funds are discounted back at a rate of 9 percent, what is the present value of her future “pot of gold”?
- Boots Adamswill receive $250,000 per year for the next 10 years as a payment for a weapon he invented. If a 6 percent rate is applied, should he be willing to sell out his future rights now for $1,750,000?

- Your grandfather has offered you a choice of one of the three following alternatives: $6,500 now; $1,000 a year for eight years; or $12,000 at the end of eight years. Assuming you could earn 7 percent annually, which alternative should you choose? If you could earn 11 percent annually, would you still choose the same alternative?

- The Baywatch Stars Company has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 20 years. Compute the current price of the bonds if the present yield to maturity is:
- 6 percent.
- 8 percent.
- 12 percent.

**NOTE: Before you calculate the answer, you should be able to tell if the answer will be above or below PAR based on the Chapter Notes for Chapter 10. **

* *

- Bloat Biochemical Co. has a $1,000 par value bond outstanding that pays 6 percent annual interest. The current yield to maturity on such bonds in the market is 5 percent. Compute the price of the bonds for these maturity dates:
*a*. 30 years.*b*. 15 years.*c*. 1 year.

**Rhetorical Question: Do you see the impact of interest rates on the value in problem 7 and the impact of the time-to-maturity on the value in problem 8?**

** **

- Mr.Bunker calls his broker to inquire about purchasing a bond of Golden Years Recreation Corporation. His broker quotes a price of $1,370 which includes a $25 stated broker’s fee. He is concerned that the bond might be overpriced based on these facts. The $ 1,000 par value bond pays 10percent interest, and it has 20 years remaining until maturity. The current yield to maturity on similar bonds is 7 percent.

Do you think the bond is overpriced? Do the necessary calculations.

- The preferred stock of Berryville State Bank pays an annual dividend of $7.50. It has a required rate of return of 8 percent. Compute the price of the preferred stock.

- Busch, Inc. issued preferred stock many years ago. It carries a fixed dividend of $100 per share. With the passage of time, yields have gone down from the original 11 percent to 7 percent (yield is the same as required rate of return).
*a*. What was the original issue price?*b*. What is the current value of this preferred stock?

- As of January 1, 2016, BancorpNorthhas had the following pattern of earnings per share over the last five years:

** Year** **Earnings per Share**

2011……………………… $4.00

2012……………………… 4.20

2013……………………… 4.41

2014……………………… 4.63

2015……………………… 4.86

The earnings per share have grown at a constant rate (on a rounded basis) and will continue to do so in the future. Dividends represent 20 percent of earnings. Project earnings and dividends for the next year (2016).

- If the required rate of return (K
_{e}) is 10 percent, what is the anticipated stock price (P_{0}) at the beginning of 2016 using formula 10-8 on page 313? - If the P/E is 16, what is the anticipated stock price?
- Which valuation makes more sense to you? Why?