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Chapter 6
Questions and Problems
• 1. Present Value and Multiple Cash Flows
• Manila Office Products has identified an
investment project with the following cash
flows, denominated in millions of pesos. If
the discount rate is 8 percent, what is the
present value of these cash flows? What is
the present value at 16 percent? At 26
percent?
• 3. Future Value and Multiple Cash Flows
• Bogata Bean Farm has identified an
investment project with the following cash
flows, denominated in thousands of pesos.
If the discount rate is 8 percent, what is
the future value of these cash flows in
Year 4? What is the future value at a
discount rate of 11 percent? At 24 percent?
• 10. Calculating Perpetuity Values
• The Perpetual Life Insurance Co. is trying
to sell you an investment policy that will
pay you and your heirs $15,000 per year
forever. If the required return on this
investment is 10 percent, how much will
you pay for the policy?
• 10.
• This cash flow is a perpetuity. To find the
PV of a perpetuity, we use the equation:
• PV = C / r
• PV = $15,000 / .10 = $150,000.00
• 11. Calculating Perpetuity Values
• In the previous problem, suppose the
Perpetual Life Insurance Co. told you the
policy costs $195,000. At what interest
rate would this be a fair deal?
• 11. Here we need to find the interest rate
that equates the perpetuity cash flows with
the PV of the cash flows. Using the PV of
a perpetuity equation:
• PV = C / r
• $195,000 = $15,000 / r
• We can now solve for the interest rate as
follows:
• r = $15,000 / $195,000 = 7.69%
• 12. Calculating EAR
• Find the EAR in each of the following
cases:
• 12.For discrete compounding, to find the
EAR, we use the equation:
•
EAR = [1 + (APR / m)]m – 1
•
EAR = [1 + (.11 / 4)]4 – 1 = 11.46%
•
EAR = [1 + (.07 / 12)]12 – 1
= 7.23%
•
EAR = [1 + (.09 / 365)]365 – 1 = 9.42%
• 13. Calculating APR
• Find the APR. or stated rate, in each of the
following cases:
• 13. Here we are given the EAR and need to find
the APR. Using the equation for discrete
compounding:
• EAR = [1 + (APR / m)]m – 1
• We can now solve for the APR. Doing so, we get:
• APR = m[(1 + EAR)1/m – 1]
• EAR = .081 = [1 + (APR / 2)]2 – 1
• APR = 2[(1.081)1/2 – 1]
= 7.94%
•
• 19. EAR versus APR
• Big Dom's Pawn Shop charges an interest
rate of 25 percent per month on loans to
its customers. Like all lenders. Big Dom
must report an APR to consumers. What
rate should the shop report? What is the
effective annual rate?
• 19.The APR is simply the interest rate per
period times the number of periods in a
year. In this case, the interest rate is 30
percent per month, and there are 12
months in a year, so we get:
• APR = 12(25%) = 300%
• To find the EAR, we use the EAR formula:
• EAR = [1 + (APR / m)]m – 1
• EAR = (1 + .25)12 – 1 = 1,355.19 %
• 20. Calculating Loan Payments
• You want to buy a new sports coupe for
€56,850, and the finance office at the
dealership has quoted you an 5.6 percent
APR loan for 60 months to buy the car.
What will your monthly payments be?
What is the effective annual rate on this
loan?
• 20.We first need to find the annuity
payment. We have the PVA, the length of
the annuity, and the interest rate. Using
the PVA equation:
• PVA = C({1 – [1/(1 + r)]t } / r)
• €56,850 = €C[1 – {1 / [1 + (.056/12)]60} /
(.056/12)]
• Solving for the payment, we get:
• C = €56,850 / 52.226 = €1,088.53
• To find the EAR, we use the EAR equation:
• EAR = [1 + (APR / m)]m – 1
• EAR = [1 + (.056 / 12)]12 – 1 = 5.75%