Mba 570 Minicase Study

Minicase Chapter Four

MBA 570

a. Draw time lines for (1) a $100 lump sum cash flow at the end of Year 2, (2) an ordinary annuity of $100 per year for 3 years, and (3) an uneven cash flow stream of -$50, $100, $75, and $50 at the end of Years 0 through 3.

LUMP-SUM AMOUNT—a single flow; for example, a $100 inflow in Year 2:

0 1 2 3 Year

100 Cash flow

ANNUITY—a series of equal cash flows occurring over equal intervals:

0 1 2 3 Year

100 100 100 +FV Ord Ann/Cash flow

UNEVEN CASH FLOW STREAM—an irregular series of cash flows that do not constitute an annuity:

0 1 2 3 Year

-50 100 75 50 + FV uneven Cash flow

b. (1) What is the future value of an initial $100 after three years if it is invested in an account paying 10 percent annual interest?

N=3 I/Y= 10% PV=-100 PMT=0 FV=?

0 1 2 3

100 FV = ?

After 1 year:

FV1 = PV + INT1 = PV + PV(I) = PV(1 + I) = $100(1.10) = $110.00.

Year 2:

FV2 = FV1 + INT2 = FV1 + FV1(I)

= FV1(1 + I) = $110(1.10) = $121.00

= PV(1 + I)(1 + I) = PV(1 + I)2.

Year 3:

FV3 = FV2 + INT3 = FV2 + FV2(k)

= FV2(1 + I) = $121(1.10) = $133.10

= PV(1 + I)2(1 + I) = PV(1 + I)3

FVn = PV(1 + i)n,

FV3 = $100(1.10)3 = $100(1.3310) = $133.10.

(2) What is the present value of $100 to be received in 3 years if the appropriate interest rate is 10 percent?

N=3 I/Y= 10% PMT= 0 FV=100 PV=?

0 1 2 3

PV = ? 100

FVn = PV(1 + k)n transforms to:

thus:

c. We sometimes need to find how long it will take a sum of money (or anything else) to grow to some specified amount. For example, if a company’s sales are growing at a rate of 20% per year, approximately how long will take sales to triple?

0 1 2 3 n = ?

-1 3

To see how long it will take to triple the money at an interest rate of 20 percent, we can use any numbers, say, $1 and $3, with this equation:

FVn = $3 = $1(1 + k)n = $1(1.20)n

d.

e....