公司理财计算题汇总

公司理财计算题汇总

金融工程三班 奚红胜

第四章：净现值：P73

Since this bond has no interim coupon payments, its present value is simply the

present value of the $1,000 that will be received in 25 years. Note: As will be discussed in the next chapter, the present value of the payments associated with a bond is the price of that bond.

PV = $1,000 /1.125 = $92.30 PV = $1,500,000 / 1.0827 = $187,780.23

a. At a discount rate of zero, the future value and present value are always the same.

Remember, FV = PV (1 + r) t. If r = 0, then the formula reduces to FV = PV. Therefore, the values of the options are $10,000 and $20,000, respectively. You should choose the second option. b. Option one: $10,000 / 1.1 = $9,090.91 Option two: $20,000 / 1.15 = $12,418.43 Choose the second option. c. Option one: $10,000 / 1.2 = $8,333.33 Option two: $20,000 / 1.25 = $8,037.55 Choose the first option.

d. You are indifferent at the rate that equates the PVs of the two alternatives.

You know that rate must fall between 10% and 20% because the option you would choose differs at these rates. Let r be the discount rate that makes you indifferent between the options.

$10,000 / (1 + r) = $20,000 / (1 + r)5 (1 + r)4 = $20,000 / $10,000 = 2

1 + r = 1.18921 r = 0.18921 = 18.921%

PV = $5,000,000 / 1.1210 = $1,609,866.18 a. $1,000 / 0.1 = $10,000

b. $500 / 0.1 = $5,000 is the value one year from now of the perpetual stream.

Thus, the value of the perpetuity is $5,000 / 1.1 = $4,545.45.

$2,420 / 0.1 = $24,200 is the value two years from now of

the perpetual stream. Thus, the value of the perpetuity is $24,200 / 1.12 = $20,000.

The easiest way to do this problem is to use the annuity factor. The annuity factor

must be equal to $12,800 / $2,000 = 6.4; remember PV =C ATr. The annuity factors are in the appendix to the text. To use the factor table to solve this problem, scan across the row labeled 10 years until you find 6.4. It is close to the factor for 9%, 6.4177. Thus, the rate you will receive on this note is slightly more than 9%. You can find a more precise answer by interpolating between nine and ten percent. [ 10% [6.1446 a r b c 6.4 d

c.