Question

Life Planning Using TVM:

Please show work so I have a better understanding.

1. You want to buy a $250,000 house 5 years from now. If you have no money to begin with, how much do you need to save at the end of each year to have 20% of the$250,000 purchase price? You plan to invest your savings with your broker who will allocate it into various asset classes. You hope to earn 8% on your money for the next 5 years. How much do you need to save at the end of each year? How does this change if you can only earn 6% return.

2. After a few years you decide that you should start saving for kid’s education. Since they will be entering college in ten years you want to match the maturity of the bond to the time when they will start college. Therefore you are considering a bond that matures in 10 years. The bond pays an 8% annual coupon. The yield on bonds of similar maturity and risk class are currently at 7%. Using the manual method to discount the cash flows (i.e. you must show the time line and the manual discounting), what is the most you will pay for the bond?

3.Even further down the road, you have enjoyed a successful career, your kids are grown and out of the house, and now you want to spend your days cruising the waterways around Wilmington. Like a lot of retirees you want to use your nest egg and have it provide a fixed income for you. Therefore you are considering investing in some bonds. One bond that you are considering has 20 years to maturity, but is callable in 10 years at $1090. Interest is paid 9% semi-annually; the bonds have a $1,000 par value; and currently sell for $950. Compute the yield to maturity and yield to call for the bonds. As an investor would you expect to get YTM or YTC?

Answer 1

1. To get 250,000 at the end of 5th year.

The base formula is we need to use compound interest formula gor each year investment separately and the formula is (1+rate of interest)^{N where N = number of years amount invested}

At 8% return if we start to invest $ 42614 each year at begining or $55480 at the end of each year we will get $250000 at the end of 5th year.

At 6% if we invest $44349 st the begning of the year or $57148 at the end of every year till 5gh year. We will receive amount $250,000 at the end of 5th year.

2.Suppose the face value is $100 to get value we need to Discount coupon payment i.e. 8 and we need to discount the at tge rate of YTM of 7%.

So the time line will be 8/(1.07ⁿ) till n =9 and for 10th year 108/(1.07¹⁰) = 111.09

3. Because the coupon is piad semi annually the rate of coupon payment will be $45 semi annual and the total period for YTM calculation will be 20×2 = 40

YTM = The rate at which present value of all the coupon payment and the maturity value is = 950(present value)

PV = 950

Coupon payment = 45

Maturity payment = 1000 + 45(last coupon value) = 1045

Number of payment = 40

YTM = 4.46%

If the bond is Callable at 1090 after 10 years then the YTC will be

PV = 950

COUPON PAYMENT = 45

Future value = 1090+45(last coupon value) = $ 1135

N payment terms = 20

YTC will be = 3.71%

As an investor i would expect to get LOWER ONE i.e. YTC