公司理财计算题汇总(2)

9% 6.4177

By interpolating, you are presuming that the ratio of a to b is equal to the ratio of c to d. (9 - r ) / (9 - 10) = (6.4177 - 6.4 ) / (6.4177 - 6.1446)

r = 9.0648%

The exact value could be obtained by solving the annuity formula for the interest rate. Sophisticated calculators can compute the rate directly as 9.0626%.

[Note: A standard financial calculator’s TVM keys can solve for this rate. With annuity

flows, the IRR key on “advanced” financial calculators is unnecessary.]

a.The annuity amount can be computed by first calculating the PV of the $25,000 which you need in five years. That amount is $17,824.65 [= $25,000 / 1.075]. Next compute the annuity which has the same present value.

$17,824.65 = C 50.07

$17,824.65 = C (4.1002) C = $4,347.26

Thus, putting $4,347.26 into the 7% account each year will provide $25,000 five years from today.

b. The lump sum payment must be the present value of the $25,000, i.e., $25,000 / 1.075 = $17,824.65 The formula for future value of any annuity can be used to solve the problem (see

footnote 11 of the text).

Option one: This cash flow is an annuity due. To value it, you must use the

after-tax amounts. The after-tax payment is $160,000 (1 - 0.28) = $115,200. Value all except the first payment using the standard annuity formula, then add back the first payment of $115,200 to obtain the value of this option.

Value

= $115,200 + $115,200 300.10

= $115,200 + $115,200 (9.4269)

= $1,201,178.88

Option two: This option is valued similarly. You are able to have $446,000 now; this is already on an after-tax basis. You will receive an annuity of $101,055 for each of the next thirty years. Those payments are taxable when you receive them, so your after-tax payment is $72,759.60 [= $101,055 (1 - 0.28)].

Value

= $446,000 + $72,759.60 300.10

= $446,000 + $72,759.60 (9.4269)

= $1,131,897.47 Since option one has a higher PV, you should choose it. se the discount factors to discount the individual cash flows. Then compute the NPV Notice that the four $1,000 cash flows form an annuity. You can still use the factor tables to compute their PV. Essentially, they form cash flows that are a six year