In: Finance
1. Solve the following questions.
a) Suppose Rosie's mum is considering purchasing a financial asset that promises to pay $2,500 per year for six years, with the first payment one year from now. The required return is 11% per year. How much should Rosie's mum pay for this asset?
b) For the year 2000, Coca-Cola Company, recorded net sales of $7,368 million. For 2010, Coca-Cola recorded net sales of $11,245 million. Over the ten-year period from the end of fiscal year 2000 to the end of 2010, What is the Coca-Cola's growth rate?
c) Leo is planning to purchase a home for $550,000 in Charleston, SC. He intends making a down payment of $50,000 and borrowing the remaining amount with a 30-year fixed rate mortgage with monthly payments. The first payment is due a month from now. The current mortgage rates are quoted at 4% per year with a monthly compounding. How much would Leo's monthly mortgage payment be?
d) Clementine is the lucky winner of the Georgia lottery of $50 million after taxes. He invests his winnings in a 10-year certificate of deposit (CD) at the Lawrenceville Credit Union. The CD promises to pay 6% per year, compounded quarterly. The credit union allows investors to reinvest the interest at that rate for the duration of the CD. How much will Clementine have at the end of ten years if his money remains invested at 6% for ten years with no withdrawals?
e) Caillou is interested in determining how long it will take an investment of $20,000 to double. The current interest rate is an interest rate of 10%?
QUESTION 1
This is basically an ordinary annuity, which pays $2,500 per year for 6 years for which we need to calculate the present value.
Present value of an annuity is mathematically represented as:
For our question, P = $2,500 r = 11%, n = 6 years, and we need to calculate PV.
Hence, substituting values, we get:
PV (or amount to be paid by Rose’s mum) = $10,576.34
QUESTION 2
This question requires application of basic time value of money function, according to which:
FV = PV * (1 + r)n
11,245 = 7,368 * (1 + r)10
(1 + r)10 = 1.5262
(1 + r) = 1.0432
r = 4.32%
QUESTION 3
This again is an example of present value of an annuity. However, here the annuity payments are monthly.
Again for application of mathematical relation in Q.1, let us define the inputs.
PV = $550,000 - $50,000 = $500,000
N = 30 years * 12 months = 360 months
R = 4% per year = 0.33% per month
We need to calculate the value of P.
Substituting values in our mathematical relation, we get:
P = $2,387.08 -- > Monthly payment for loan servicing
QUESTION 4
This question requires application of basic time value of money function, according to which:
FV = PV * (1 + r)n
PV = $50 mil
R = 6%/4 = 1.5% per quarter
N = 10 years * 4 quarters = 40 quarters
FV = 50 * (1 + 0.015)40
FV = $90.70 mil
QUESTION 5
We will again use basic TVM function here to calculate n:
40000 = 20000 * (1 + 10%)n
2 = (1.1)n
Taking log on both sides
ln (2) = n ln (1.1)
n = 7.27 years
It would take 7.27 years to double the invested amount at 10% per annum.