Sullivan University HCA 545 – Pensacola Surgery Centers Time Value Analysis

1. Consider the $50,000 excess cash. Assume
that Gary invests the funds in a one-year CD.
a.What is the CDs
value at maturity (future value) if it pays 10.0 percent (annual) interest?
b. What would be
its future value if the CD pays 5.0 percent interest? It pays 15.0 percent
interest?
c. Bank South
offers CDs with 10.0 percent nominal (stated) interest, but compounded semiannually.
What is the effective annual rate on this CD? What would the future value be
after one year if $50,000 were invested?
d. The Pensacola Branch of Bank of America
offers a 10.0 percent CD with daily compounding. What is the CDs
effective annual rate and its value at maturity one year from now if
$50,000 is invested? (Assume a 365 day year)

2. Rework Parts (a) through (d) of Question 1
assuming that each CD has a five-year maturity.
a. FV = PV x (1 + i)n
b. FV = PV x (1 +
i)n
c. FV = PV x (1
+i/m)n x m
d.FV = PV x (1 +i/m)n x m

3. Now consider the Surgery Centers goal of having $200,000
available in five years to buy a new patient billing system.
a. What lump sum
amount must be invested today in a CD paying 10.0 percent annual interest
to accumulate the needed $200,000?
b. What annual
interest rate is needed to produce $200,000 after five Years if only
$100,000 is invested?

4. Now consider a second alternative for
accumulating funds to buy the new billing system. In lieu of a lump sum
investment, assume that five annual payments of $32,000 are made at the
end of each year.
a. What type of
annuity is this?
b. What is the
present value of this annuity if the opportunity cost rate is 10.0 percent
annually? 10.0 percent compounded semiannually?
c. What is the
future value of this annuity if the payments are invested in an account paying
10.0 percent annually? 10.0 percent compounded semiannually?
d. What annual
interest rate is required to accumulate the $200,000 needed to make the purchase
assuming a $32,000 annual payment?
e. What size annual
payment would be needed to accumulate $200,000 under annual compounding
at a 10.0 percent rate?
f. Suppose the payments are only $16,000 each,
but they are made Every six months, starting six months from now. What
would be the future value if the ten payments were invested at 10.0
percent interest? If they were invested at BankSouth at 10.0 percent
compounded semiannually?

5. Assume now that the payments are made at the
beginning of each period. Repeat the analysis in Question 4.
a. An annuity due
is a series of cash flows that occur at the beginning of an accounting period.

6. Now consider the uneven cash flow stream
stemming from the lease agreement given in the case.
a. what is the
present (year 0) value of the annual lease cash flows if the opportunity cost
rate is 10.0 percent annually?

What is the value of this cash flow stream at the end of year
5 if the cash flows are invested at 10.0 percent annually? What is the
present value of this future value when discounted at 10.0 percent? What
does this result indicate about the consistency inherent in the time
value analysis?
c. Does the office
renovations and subsequent lease arrangement appear to be a good investment
for the company? (Hint: Compare the
cost of renovation with the present value of the lease payments)

7. Now assume that it is five years later and
the company was unable to accumulate the $200,000 needed to make the
software purchase. Instead, the company is forced to borrow the $200,000.
The loan calls for repayment in equal annual installments over a four-year
period, with the first payment due at the end of one year. Assuming that
the firm can borrow the funds at a 10.0 percent rate, what amount of
interest and principal will be repaid at the end of each year of the
loan?

Throughout this case, you have been either discounting or
compounding cash flows. Many financial analyses, such as bond refunding
decisions, capital investment decisions, and lease decisions, involve
discounting projected future cash flows. What is the appropriate rate in
such situations? What factors influence the value of this rate?