Principles of Corporate Finance 7 E Solution Manual
CHAPTER 3
How to Calculate Present Values
Answers to Practice Questions
1.
a.
PV = $100 0.905 = $90.50
b.
PV = $100 0.295 = $29.50
c.
PV = $100 0.035 = $ 3.50
d.
PV = $100 0.893 = $89.30
PV = $100 0.797 = $79.70
PV = $100 0.712 = $71.20
PV = $89.30 + $79.70 + $71.20 = $240.20
2.
a.
PV = $100 4.279 = $427.90
b.
PV = $100 4.580 = $458.00
c. We can think of cash flows in this problem as being the difference between two separate streams of cash flows. The first stream is $100 per year received in years 1 through 12; the second is $100 per year paid in years 1 through 2.
The PV of $100 received in years 1 to 12 is: PV = $100 [Annuity factor, 12 time periods, 9%] PV = $100 [7.161] = $716.10 The PV of $100 paid in years 1 to 2 is: PV = $100 [Annuity factor, 2 time periods, 9%] PV = $100 [1.759] = $175.90
Therefore, the present value of $100 per year received in each of years 3 through 12 is: ($716.10 - $175.90) = $540.20. (Alternatively, we can think of this as a 10‑year annuity starting in year 3.)
3. a. so that r1 = 0.136 = 13.6% b. c. AF2 = DF1 + DF2 = 0.88 + 0.82 = 1.70
d. PV of an annuity = C [Annuity factor at r% for t years] Here:
$24.49 = $10 [AF3]
AF3 = 2.45
e. AF3 = DF1 + DF2 + DF3 = AF2 + DF3
2.45 = 1.70 + DF3
DF3 = 0.75
4. The present value of the 10-year stream of cash inflows is (using Appendix Table 3): ($170,000 5.216) = $886,720 Thus: NPV = -$800,000 + $886,720 = +$86,720 At the end of five years, the factory’s value will be the present value of the five remaining $170,000 cash flows. Again using Appendix Table 3:
PV = 170,000 3.433 = $583,610
5. a. Let St = salary in year t
b. PV(salary) x 0.05 = $18,911.
Future value = $18,911 x (1.08)30 = $190,295
c. Annual payment = initial value annuity factor 20‑year annuity factor at 8 percent = 9.818 Annual payment = $190,295/9.818 = $19,382
6.
Period
How to Calculate Present Values
Answers to Practice Questions
1.
a.
PV = $100 0.905 = $90.50
b.
PV = $100 0.295 = $29.50
c.
PV = $100 0.035 = $ 3.50
d.
PV = $100 0.893 = $89.30
PV = $100 0.797 = $79.70
PV = $100 0.712 = $71.20
PV = $89.30 + $79.70 + $71.20 = $240.20
2.
a.
PV = $100 4.279 = $427.90
b.
PV = $100 4.580 = $458.00
c. We can think of cash flows in this problem as being the difference between two separate streams of cash flows. The first stream is $100 per year received in years 1 through 12; the second is $100 per year paid in years 1 through 2.
The PV of $100 received in years 1 to 12 is: PV = $100 [Annuity factor, 12 time periods, 9%] PV = $100 [7.161] = $716.10 The PV of $100 paid in years 1 to 2 is: PV = $100 [Annuity factor, 2 time periods, 9%] PV = $100 [1.759] = $175.90
Therefore, the present value of $100 per year received in each of years 3 through 12 is: ($716.10 - $175.90) = $540.20. (Alternatively, we can think of this as a 10‑year annuity starting in year 3.)
3. a. so that r1 = 0.136 = 13.6% b. c. AF2 = DF1 + DF2 = 0.88 + 0.82 = 1.70
d. PV of an annuity = C [Annuity factor at r% for t years] Here:
$24.49 = $10 [AF3]
AF3 = 2.45
e. AF3 = DF1 + DF2 + DF3 = AF2 + DF3
2.45 = 1.70 + DF3
DF3 = 0.75
4. The present value of the 10-year stream of cash inflows is (using Appendix Table 3): ($170,000 5.216) = $886,720 Thus: NPV = -$800,000 + $886,720 = +$86,720 At the end of five years, the factory’s value will be the present value of the five remaining $170,000 cash flows. Again using Appendix Table 3:
PV = 170,000 3.433 = $583,610
5. a. Let St = salary in year t
b. PV(salary) x 0.05 = $18,911.
Future value = $18,911 x (1.08)30 = $190,295
c. Annual payment = initial value annuity factor 20‑year annuity factor at 8 percent = 9.818 Annual payment = $190,295/9.818 = $19,382
6.
Period