公司理财 作业

公司理财第二次作业 第四组（黑米组）共同完成

组长：王赛

组员：王遨寰，孙玲玲，李娜，李静，徐蕾，幸国全

13.a. If the one-year discount factor is .905, what is the one-year interest rate? a. ⇒=+=0.905r 11DF 1

1r 1 = 0.1050 = 10.50%.

b. If the two-year interest rate is 10.5%, what is the two-year discount factor? b. 0.819.(1.105)

1)r (11DF 2222==+=

c. Given these one- and two-year discount factors, calculate the two-year annuity factor. c.AF 2 = DF 1 + DF 2 = 0.905 + 0.819 = 1.724.

d. If the PV of $10 a year for three years is $24.65, what is the three-year annuity factor? PV of an annuity = C ⨯ [annuity factor at r % for t years].Here:

$24.65 = $10 ⨯ [AF 3]

AF 3 = 2.465

e. From your answers to (c) and (d), calculate the three-year discount factor.

AF 3 = DF 1 + DF 2 + DF 3 = AF 2 + DF 3

2.465 = 1.724 + DF 3

DF 3 = 0.741

14.A factory costs $800,000. You reckon that it will produce an inflow after operating costs of $170,000 a year for 10 years. If the opportunity cost of capital is 14%, what is the net present value of the factory? What will the factory be worth at the end of five years? The present value of the 10-year stream of cash inflows is

6$886,739.6(1.14)0.1410.141 $170,000PV 10=⎥⎦

⎤⎢⎣⎡⨯-⨯=

Thus:

NPV = –$800,000 + $886,739.66 = +$86,739.66

At the end of five years, the factory’s value will be the present value of the five remaining $170,000 cash flows:

6$583,623.7(1.14)0.1410.141 $170,000PV 5=⎥⎦

⎤⎢⎣⎡⨯-⨯=

15.A machine costs $380,000 and is expected to produce the following cash flows:

If the cost of capital is 12%, what is the machine’s NPV?

$23,696.151.12$50,0001.12$68,0001.12$80,0001.12$92,0001.12$92,000 1.12$85,000 1.12$80,0001.12$75,0001.12$57,0001.12$50,000$380,000(1.12)C NPV 1098765

43210

t t t =+++++

+++++-==∑=0

16. Mike Polanski is 30 years of age and his salary next year will be $40,000. Mike forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60.

a. If the discount rate is 8%, what is the PV of these future salary payments? Let S t = salary in year t.

∑=-=301t t

1t (1.08)(1.05)40,000PV 3$760,662.5(1.08).05)-(.08(1.05).05)-(.081 43030

=⎥⎦

⎤⎢⎣⎡⨯-⨯=000,0 b. If Mike saves 5% of his salary each year and invests these savings at an interest rate of 8%, how much will he have saved by age 60?

b.

PV(salary) x 0.05 = $38,033.13

Future value = $38,033.13 x (1.08)30 = $382,714.30

c. If Mike plans to spend these savings in even amounts over the subsequent 20 years, how much can he spend each year?

$38,980.30 (1.08)0.0810.081$C (1.08)0.0810.081 C $r)(1r 1r 1 C PV 2020t =⎥⎥⎦⎤⎢⎢⎣⎡⨯-=⎥⎦

⎤⎢⎣⎡⨯-⨯=⎥⎦

⎤⎢⎣⎡+⨯-⨯=382,714.30

382,714.30