## Question

Assignment 1: Time Value Analysis

1. Calculate the following values for a lump sum assuming annual compounding(10 Points):

a. The future value of $300 invested at 6% for three years

b. The future value of $400 invested at 7% for ten years

c. The future value of $400 invested at 10% for seven years

d. (1 point) What do you notice about the future values of b and c compared to their original $400 value?

2. Now assume that interest compounds quarterly and calculate the values for a lump sum (10 points):

a. The future value of $300 invested at 6% for three years (twelve quarter-years if you will)

b. The future value of $400 invested at 10% for seven years

c. Compare your answer for 1b and 2b, how does the frequency of compounding affect future values? Why?

3. (3 points) What is the effective annual rate (EAR) if 9% interest compounds

a. semi-annually,

b. quarterly

c. monthly

4. (7 points) Suppose you have a $600 six-year loan at 8% annual interest and with $100 annual principal payments due at the end of each year (interest compounds annually). How much interest expense would you save if you made quarterly payments of $25 per quarter and interest compounded quarterly?

5. (10 points) Construct a time line that depicts the cash flows for a loan with the following parameters:

a. Principal Loan amount at its initial distribution: $3000

b. Term of the Loan: 4 years

c. Annual Interest rate: 7% on remaining principal, payments are made annually

d. Principal payments of $500 are due at the end of each of the first three years of the loan

e. A “Balloon” payment for the remaining principal is due at the end of the fourth year.

(Hint: This is easier to do if you separately calculate and show the interest and principal payments; you have to calculate the final “balloon” payment on the loan).

6. (10 points) Find the values assuming a regular or ordinary annuity:

a. The present value of $600 per year for eight years at 12 percent

b. The future value of $600 per year for ten years at 9 percent

7. (10 points) Consider the following uneven cash flow stream:

Year Cash Flow

0 $1,000

1 $500

2 $600

3 $0

4 $900

a. What is the present (year 0) value of the cash flow stream if the annual opportunity cost rate is 8 percent?

b. What is the future value (year 4) of the cash flow stream if the cash flows are invested in an account that pays 8 percent annually?

8. (10 points) Abercombie Hospital has just settled litigation. It will receive $15 million dollars in twelve equal installments from Snodgrass Medical Equipment for twelve years in equal installments of $1,250,000 beginning in one year (i.e. it receives no payment at time zero; it receives its first payment twelve months hence from time zero)

a. If the rate of return is four percent annually, what is the present value of the litigation settlement?

b. If the rate of return is six percent annually, what is the present value of the litigation settlement?

9. (10 points) North Jersey Health has just borrowed $600,000 on an eight year payment term loan at an six percent annual interest rate. The first payment is due one year. Construct the amortization schedule for this loan.

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