Chapter 2 How to Calculate Present Values
CHAPTER 2
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507*1.126 = $1
2. 125/139 = .899
3. PV = 374/(1.09)9 = 172.20
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003
5. FV = 100*1.158 = $305.90
6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40
8. a. PV = 1/.10 = $10
b. Since the perpetuity will be worth $10 in year 7, and since that is roughly double the present value, the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)
c. A perpetuity paying $1 starting now would be worth $10, whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these cash flows is therefore approximately $5. PV = 10 – 5= $5 (approximately)
d. PV = C/(r-g) = 10,000/(.10-.05) = $200,000.
9. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does not appreciate over those five years).
b. You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 = $55,476.
c. At the end of 6 years you would have 1.086 × (60,476 - 55,476) = $7,934.
10. We did not cover continuous compounding so you do not need to worry about this question.
11. Same as
How to Calculate Present Values
Answers to Problem Sets
1. If the discount factor is .507, then .507*1.126 = $1
2. 125/139 = .899
3. PV = 374/(1.09)9 = 172.20
4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1,003
5. FV = 100*1.158 = $305.90
6. NPV = -1,548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40
8. a. PV = 1/.10 = $10
b. Since the perpetuity will be worth $10 in year 7, and since that is roughly double the present value, the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately)
c. A perpetuity paying $1 starting now would be worth $10, whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these cash flows is therefore approximately $5. PV = 10 – 5= $5 (approximately)
d. PV = C/(r-g) = 10,000/(.10-.05) = $200,000.
9. a. PV = 10,000/(1.055) = $7,835.26 (assuming the cost of the car does not appreciate over those five years).
b. You need to set aside (12,000 × 6-year annuity factor) = 12,000 × 4.623 = $55,476.
c. At the end of 6 years you would have 1.086 × (60,476 - 55,476) = $7,934.
10. We did not cover continuous compounding so you do not need to worry about this question.
11. Same as