Chapter 4 of corporate finance

Chapter 4
15. For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR / m)]m – 1
= .0719, or 7.19%
EAR = [1 + (.07 / 4)]4 – 1
EAR = [1 + (.16 / 12)]12 – 1
= .1723, or 17.23%
= .1163, or 11.63%
EAR = [1 + (.11 / 365)]365 – 1
To find the EAR with continuous compounding, we use the equation:
EAR = er – 1
EAR = e.12 – 1 = .1275, or 12.75%
23.

Although the stock and bond accounts have different interest rates, we can draw one time line, but we need to remember to apply different interest rates. The time line is:
0

1

Stock
Bond

$800
$350

360

361

...

660
…

$800
$350

$800
$350

$800
$350

$800
$350

C

C

C

We need to find the annuity payment in retirement. Our retirement savings ends at the same time the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs.
Stock account: FVA = $800[{[1 + (.11/12) ] 360 – 1} / (.11/12)] = $2,243,615.79
Bond account: FVA = $350[{[1 + (.06/12) ] 360 – 1} / (.06/12)] = $351,580.26
So, the total amount saved at retirement is:
$2,243,615.79 + 351,580.26 = $2,595,196.05
Solving for the withdrawal amount in retirement using the PVA equation gives us:
PVA = $2,595,196.05 = C[1 – {1 / [1 + (.08/12)]300} / (.08/12)]
C = $2,595,196.06 / 129.5645 = $20,030.14 withdrawal per month
26. This is a growing perpetuity. The present value of a growing perpetuity is:
PV = C / (r – g)
PV = $175,000 / (.10 – .035)
PV = $2,692,307.69
It is important to recognize that when dealing with annuities or perpetuities, the present value equation calculates the present value one period before the first payment. In this case, since the first payment is in two years, we have calculated the present value one year from now. To find the value today, we simply discount this value as a lump sum. Doing so, we find the value of