Question

A) Sydney wants to establish a savings. plan that will accomplish two tasks. First, he would like to purchase a new car at the end of five years from now for $30,000. Second, he would like to retire at the end of 15 years from now with enough money to provide him with a pretax income of $40,000 per year for ten years after retirement. Sydney can save $8,000 per year for the first five years. How much would he have to invest (supposing interest rates remain at 10% per year over the entire time period above) each year from years 6 through 15 to accomplish his goals?

B) Impossible Inc. has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend t6 be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are $3 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 6 percent. If the firm's investors expect to earn a return of 14 percent on this stock, what must be its price today?

In October of 2013, Jacob Industries borrowed funds by selling bonds with a $1,000 face value. At issue, the bonds had 10 years to maturity, and bore a coupon rate of 16%, paid semiannually. At the time, the yield to maturity of the bonds was 14%. In October of 2017, interest rates had fallen and the yield on bonds of the same level of risk as those of Jacob Industries had dropped to 12%. If you could sell the bonds in October of 2017, what would each be worth?

Answer 1

Question (A).

Amount required after 15 years towards retirement plan is the PV of annuity for 10 years ascertained at $245.782.68 as follows:

Savings of $8,000 per year will accumulate to $48,840.80 at the end of 5 years as follows:

Amount required for purchasing car at the end of 5 years= $30,000.

Therefore, surplus available after purchasing car= $48,840-$30,000 = $18,840

This amount will have a future value of $ 48,866.11 at the end of 10 years from that date (ie., 15 years from now) as follows:

Hence the corpus to be built over 10 years (after the initial 5 years)= $245,782.68- $48,866.11 =$196,916.57

Amount to be invested at the end of years 6 to 15 (10 payments) is ascertained at $12,355.61 as follows:

Question (B):

The Price today is $31.27 ascertained using the two stage dividend discount model as follows:

Question 3: Price of the bond in October 2017 is $1,167.68 ascertained using the PV function of Excel as follows: