Optimizing Net Present Value Using Continuous Compounding

The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of $P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?

Solution Preview

The goal is to maximize the net present value of the sale of the wine.
Revenue is given in the question

Revenue = P * (1 + 20 sqrt(t))

Revenue must be discounted by the time value of money, in this case 5% compounded continuously. This discount factor is ...

Solution Summary

The solution provides a detailed look at optimizing the Net Present Value of an appreciating asset. The solution uses continuous compounding to discount the future cash flow. Basic concepts of differential calculus as used as well as solving quadratic equations.

Show the formula used in the following questions in detail
1)
a. What is the future value of $4,000 invested at 6% for 22 years with annual compounding?
b. What is the future value of $4,000 invested at 6% for 22 years with monthly compounding?
c. What is the future value of $4,000 invested at 6% for 22 years with cont

25. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?
A. annual compounding
B. monthly compounding
C. daily compounding
D. continuouscompounding
E. It is impossible to tell without knowing the term of the loan.

suppose the deposit $20,000 for 5 yrs @ 8% rate what is the return annually (n = 1) and quarterly (n = 4).
Round both to the hundredth place.
c) Does compounding annually or quarterly yield more interest and explain
d) if a bank compounds continuously the the formula used is A=Pe^rt where e is a constant and equals

1. Calculate the return (A) if the bank compounds daily (n = 365). Round the answer. using this formula:
A=P(1+r/n)^ nt
2. If a bank compounds continuously, then the formula takes a simpler, that is A= P e(n)squared where e is a constant and equals approximately 2.7183. Calculate A with continuouscompounding

You make deposits of $2 each year for 30 years. The rate of interest that will prevail is 10 percent for the first 20 years and then 12 percent for the remaining period. If the interest rate is compounded continuously, what is the present and future value of these deposits.

These questions are adapted from Fundamentals of Futures and Options Markets, 7th ed., John C. Hull.
Chapter 4
The 6-month, 12-month, 18-month, and 24-month zero rates are 3.00%, 3.50%, 4.00%, and
4.50% with semi-annual compounding.
Q I: What are the rates with continuouscompounding?
Q2: What is the forward rate fo

1.)The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $25,000 per year forever. If the required return on the investment is 7.2 percent, how much will you pay for the policy?
2.)In the previous problem, suppose a sales associate told you the policy costs $375,000. At w

A small business expects an income stream of $5000 per year for a four-year period.
a) Find the presentvalue of the business if the annual interest rate compounded continuously is:
(1) 3%
(2) 10%
b) in each case, find the value of the business at the end of the four-year period.

Using Microsoft Excel, calculate the total amount you will receive in a year if you invest $1,000 now (assuming the interest rate is 8% per annum) at:
a. yearly compounding
b. semiannually compounding
c. quarterly compounding
d. daily compounding