1. Assume that Alessi Balsamic Vinegar sells for $3.50 for a 4 year old bottle a
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Question
1. Assume that Alessi Balsamic Vinegar sells for $3.50 for a 4 year old bottle and that a 20 year old bottle sells for $10.50. Calculate the annual rate of return that the company is expecting to earn. Show your work. Do not use a calculator with a built-in function for calculating rate of return. You can use a calculator for natural logarithms and Euler’s constant. Hint: use natural logarithms.
2)Calculate the levelized payment for a $1 annuity lasting 50 years growing at 3% and discounted at 5%. Show your work, using the technique that I showed you in class.
Explanation / Answer
(1)
If r: Annual rate of return, then
Price of 4-year bottle = Price of current year bottle x (1 + r)4 = $3.5 .... (1)
Price of 20-year bottle = Price of current-year bottle x (1 + r)20 = $10.50 ..... (2)
Dividing (2) by (1):
10.50 / 3.5 = (1 + r)5
(1 + r)5 = 3
Taking natural logarithms of both sides,
5 ln(1 + r) = ln 3
ln (1 + r) = ln 3 / 5 = 0.4771 / 5 = 0.0954
(1 + r) = e0.0954 = 1.10
r = 1.10 - 1 = 0.10 or 10%
(2)
The gradient by which the annuity grows each year is = (1 + growth rate) / (1 + discount rate)
= 1.03 / 1.05 = 0.03
So, the present value of cash flow series will be:
PV = A + 0.03A + (0.03)2A + (0.03)3A + ....... + (0.03)49A where A: Annuity = $1
Note: In absence of exact technique used in your class, I cannot proceed further.
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