Question

I will not give credit for any unsupported answer -- even if it is correct!!. All cash flows are end-of-period unless otherwise stated .

Problems 1 and 2 relate to this information :

The current monthly income statement for JRT, Inc., represents the results of selling 8,000 coffee mugs: Sales (revenue) $56,000 Cost of goods sold (33,000) Gross margin $23,000 S & A expenses (16,000) Income before taxes $ 7,000 Income taxes (@ 30%) (2,100) Net income $ 4,900 Cost of goods sold included fixed manufacturing costs of $5,000, while selling and administrative expenses (“S & A expenses”) included $4,000 of fixed costs. Sales commissions amounting to $0.40 per coffee mug were also included in S & A expenses.

1. How many coffee mugs would JRT need to sell to earn a monthly net income of $7,000?

2. JRT received a special order for 3,000 coffee mugs from the Lyric Opera of Chicago (Lyric). JRT would not have to pay a sales commission on these mugs, but would have to place a special “Lyric” design on each mug at a cost of $0.50 per mug. In addition, the fixed cost of setting up this order would amount to $1,900. If the Lyric agreed to pay only $6.00 per mug, what would be the effect on JRT’s monthly net income if they accepted this order?

3. You are considering purchasing a fifteen-year annuity that offers annual payments of $9,000 with the first payment occurring one year from today. You expect that interest rates will be 5% per annum for the first five-year period, 6.5% per year for the second five-year period, and 8% for the third five-year period. What is the most that you would pay for this investment today, i.e., its present value?

4. You just sold a piece of property. The buyer offers you a choice between accepting $100,000 immediately followed by payments of $50,000 at the end of each year for fifteen years (#1). Alternatively, you could receive $150,000 now and payments of only $43,500 annually for fifteen years ( #2).

a. Which alternative would you prefer a. if your required rate of return is eight percent?

b. If your required rate of return is thirteen percent?

c. At what required rate of return would these two investments have the same present value?

5. You plan on retiring forty years after you begin your first job and wish to have $2,500,000 at retirement. You intend to make your first payment at the end of your first year on the job and then increase your payments by 3 percent annually thereafter. If you invest in a fund paying an annual percentage rate (APR) of six percent, compounded semiannually, what is the amount of the first payment necessary to reach your objective ?

6. Fast forward: You have just retired and reached your objective (see above) of accumulating $2,500,000 in your retirement fund. You expect to live for another thirty years (exactly) and wish to leave $1,000,000 to Illinois Tech when you are gone. What is the most that you could withdraw from this fund at the end of each month and still leave the money to Tech? The fund is expected to return eight per annum, compounded monthly?

7. You have been following a company, AmazingDotCom, Inc., that is about to go public this afternoon. You believe that the company will not pay any dividends for the first eight years of its operations. At the end of the ninth year, you foresee receiving $1 per share as a dividend. You forecast that the tenth year’s dividend will be $1.75 per share and after that dividends will grow at an annual rate of 2-1/2 percent forever. What would you pay for a share of this stock today if you wished to earn twenty percent per annum on your investment?

8. On June 30, 2018, you closed on your new condominium and obtained a $250,000 thirty year mortgage at an APR of 4.32%. The first monthly payment was due at that time (June 30, 2018), and then on the last day of each month thereafter (this is an “annuity in advance” or an “annuity due”).

a. What was the amount of your required monthly payment?

b. Assuming that you made all payments exactly when due, how much interest would you have paid on the mortgage in the year ending December 31, 2018?

c. How much interest would you pay in 2019 if you made all of your scheduled payments exactly when due?

d. If the interest rate were to increase to 4.62% after sixty payments, what would be the amount of your new monthly payment? (the life of the mortgage would be unchanged).

9. You are working on your income taxes and want to figure your mortgage interest deduction for the previous year. Unfortunately someone inadvertently ran your mortgage documents through a shredder. You were able to discover fragments of the amortization schedule that showed elements from a row from that schedule:

Payment# =100

Amount = $1,932.90

Interest = ???

Principal = $709.30

Balance = $244,010.90

a. Determine the APR of this mortgage (two three decimal places);

b. Determine the original amount of the mortgage;

c. Determine the original term (length) of the mortgage; d. Complete the following row of the mortgage’s amortization schedule:

Payment # = 200

Amount = ??

Interest = ??

Principal = ??

Balance = ??

10. You are considering lending some money to a company that offers to make semiannual payments of $4,000 to you for thirty years and then pay you $100,000 at the end of the thirtieth year. How much would you lend to this company if

a. you required an APR of ten percent compounded semiannually?

b. you required an APR of six percent compounded semiannually?

c. you required an APR of eight percent compounded semiannually?

Answer 1

Solution to Question 1

From the given details, we have the following calculations

Given:

(i) Sales revenue from selling 8000 coffee mugs = $56,000

Selling price of one coffee mug = $7

(ii) Cost of goods sold includes a fixed cost of $5,000.

Cost of goods sold for 8000 coffee mugs = $33,000 - $5,000 = $28,000

(iii) S & A Expenses included fixed cost of $4,000.

S & A Expenses (including sales commissions) for 8000 coffee mugs = $16,000 - $4,000 = $12,000

Total variable cost for 8000 coffee mugs = $28,000 + $12,000 = $40,000

Variable cost for each coffee mug =

Calculating backwards to arrive at the number of mugs to be sold.

Income taxes = 30% of Net income before taxes

Net profit = 70% of net income before taxes

From our problem,

70% of Net income before taxes = 7000

Net income before taxes = ............................(a)

Now, let "X" be the number of coffee mugs sold.

Sales revenue = 7X.........................(b)

Cost of goods sold = Fixed cost + Variable cost = 5000 + Variable Cost of goods sold

S & A Expenses = Fixed cost + Variable Cost = 4000 + Variable S&A Expenses

Total Cost (including Cost of goods sold and S&A Expenses) = 9000 + Total variable cost

= 9000 + 5X.......................(c)

(Where variable cost for each coffee mug = $5, as calculated above)

(b) - (c) gives us the value of net income before taxes.

Equating and solving, we have

(b) - (c) = (a)

We can cross check our answer from the following calculations