What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly? | CourseHero Help
PROBLEM 1
Find the following values for a lump sum:
The future value of $500 invested at 8 percent for one year
The future value of $500 invested at 8 percent for five years
The present value of $500 to be received in one year when the opportunity cost rate is 8 percent
The present value of $500 to be received in five years when the opportunity cost rate is 8 percent
assuming:
- Annual compounding
- Semiannual compounding
- Quarterly compounding
PROBLEM 2
What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly?
ANSWER
PROBLEM 3
Find the following values assuming a regular, or ordinary, annuity:
The present value of $400 per year for ten years at 10 percent
The future value of $400 per year for ten years at 10 percent
The present value of $200 per year for five years at 5 percent
The future value of $200 per year for five years at 5 percent
assuming:
- A regular or ordinary annuity
- An annuity due
ANSWER
PROBLEM 4
Consider the following uneven cash flow stream:
Year Cash Flow
0 $0
1 $250
2 $400
3 $500
4 $600
5 $600
- What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent?
- AID an outflow (or cost) of $1,000 at Year 0. What is the present value (or net present value) of the
stream?
ANSWER
PROBLEM 5
Consider another uneven cash flow stream:
Year Cash Flow
0 $2,000
1 $2,000
2 $0
3 $1,500
4 $2,500
5 $4,000
- What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?
- What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an
account that pays 10 percent annually?
- What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000
at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.)
- Time value analysis involves either discounting or compounding cash flows. Many healthcare financial
management decisionssuch as bond refunding, capital investment, and lease versus buyinvolve
discounting projected future cash flows. What factors must executives consider when choosing a
discount rate to apply to forecasted cash flows?
ANSWER
PROBLEM 6
What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent?
Suppose that interest rates doubled in the economy and the appropriate discount rate is now 14 percent.
What would happen to the present value of the perpetuity?
ANSWER
PROBLEM 7
An investment that you are considering promises to pay $2,000 semiannually for the next two years,
beginning six months from now. You have determined that the appropriate opportunity cost (discount)
rate is 8 percent, compounded quarterly. What is the present value of this investment?
ANSWER
PROBLEM 8
Consider the following investment cash flows:
Year Cash Flow
0 -$1,000
1 $250
2 $400
3 $500
4 $600
5 $600
- What is the return expected on this investment measured in dollar terms if the opportunity cost rate is
10 percent?
- Provide an explanation, in economic terms, of your answer.
- What is the return on this investment measured in percentage terms?
- Should this investment be made? Explain your answer.
ANSWER
PROBLEM 9
Epitome Healthcare has just borrowed $1,000,000 on a five-year, annual payment term loan at a 15
percent rate. The first payment is due one year from now. Construct the amortization schedule for this
loan.
ANSWER
Chapter 5
PROBLEM 1
Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine:
State of the Probability Rate of
economy of occurrence return
Very poor 0.1 -10%
Poor 0.2 0%
Average 0.4 10%
Good 0.2 20%
Very good 0.1 30%
- What is the expected rate of return on the project?
- What is the projects standard deviation of returns?
- What is the projects coefficient of variation (CV) of returns?
- What type of risk does the standard deviation and CV measure?
- In what situation is this risk relevant?
ANSWER
PROBLEM 5
A few years ago, the Value Line Investment Survey reported the following market betas for the stocks of
selected healthcare providers:
Company Beta
Quorum Health Group 0.90
Beverly Enterprises 1.20
HEALTHSOUTH Corporation 1.45
United Healthcare 1.70
At the time these betas were developed, reasonable estimates for the risk-free rate, RF, and the required rate of return on the market, R(Rm), were 6.5 percent and 13.5 percent, respectively.
- What are the required rates of return on the four stocks?
- Why do their required rates of return differ?
- Suppose that a person is planning to invest in only one stock rather than hold a well-diversified stock
portfolio. Are the required rates of return calculated above applicable to the investment? Explain your
answer.
