1. Time Value of Money
Multiple Cash Flows

2. Q 1)
First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually.    If you made a deposit of $16,500 in each bank, how much more money would you earn from your Second City Bank account at the end of 12 years?
The simple interest per year is:   $16,500 × .07 = $1,155   So, after twelve years, you will have:   $1,155 × 12 = $13,860 in interest.   The total balance will be:   Total balance = $16, ,860 Total balance = $30,360 With compound interest, we use the future value formula:   FV = PV(1 + r)t FV = $16,500(1.07)12 FV = $37,   The difference is:   Difference = $37, – 30,360 Difference = $6,801.16

3. Q 2) For each of the following, compute the present value: ? 11 5 % $
Years
Interest Rate
Future Value ? 11 5 % $
18,628 3 10
42,817 15 13
803,382 20 12
660,816
18,628
42,817
803,382
660,816

4. Q 3)
You’re trying to save to buy a new $205,000 Ferrari. You have $34,000 today that can be invested at your bank. The bank pays 4.1 percent annual interest on its accounts.    How long will it be before you have enough to buy the car?
To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:    FV = PV(1 + r)t Solving for t, we get:    t = ln(FV / PV) / ln(1 + r) FV = $205,000 = $34,000(1.041)t t = ln($205,000 / $34,000) / ln1.041 t = years

5. Q 4)
Investment X offers to pay you $7,900 per year for 9 years, whereas Investment Y offers to pay you $10,800 per year for 5 years.
If the discount rate is 8 percent, what is the present value of these cash flows?
If the discount rate is 20 percent, what is the present value of these cash flows?
The times lines are:  
PV$7,900$7,900$7,900$7,900$7,900$7,900$7,900$7,900$7,900 
012345PV$10,800$10,800$10,800$10,800$10,800  To find the PVA, we use the equation: PVA = C({1 – [1 / (1 + r)t]} / r)   At an interest rate of 8 percent: PVA = $7,900{[1 – (1 / 1.089) ] / .08 } = $49, PVA = $10,800{[1 – (1 / 1.085) ] / .08 } = $43,   And at an interest rate of 20 percent: PVA = $7,900{[1 – (1 / 1.209) ] / .20 } = $31, PVA = $10,800{[1 – (1 / 1.205) ] / .20 } = $32,   Notice that the PV of Investment X has a greater PV at an interest rate of 8 percent, but a lower PV at an interest rate of 20 percent. The reason is that X has greater total cash flows. At a lower interest rate, the total cash flow is more important since the cost of waiting (the interest rate) is not as great. At a higher interest rate, Y is more valuable since it has larger annual payments. At a higher interest rate, getting these payments early is more important since the cost of waiting (the interest rate) is so much greater.

6. Q 5)
Eulis Co. has identified an investment project with the following cash flows
If the discount rate is 11 percent, what is the present value of these cash flows?
What is the present value at 16 percent?
What is the present value at 22 percent
Year
Cash Flow 1
$1,070 2
910 3
1,480 4
1,840