1
a. One payment of coupon; 10% of €1000,- = €100,-
The payments are an annuity; .05 x (1 – .05 20) = €1246.22
b. PV of the bond = PV of the coupons + PV of the face value
PV of the bond = 1246.22 + .05 20 = 1246.22 + 376.89 = 1623.11
c. .0519 + .05 x (1 – .0519) + 100 = €1704.27
d. Answer c – 100 = €1604.27
2
a. The yield to maturity as an effective semi-annual rate is the same as the APR; 8%
The yield to maturity as an effective annual rate is (1 + 0..5) 0.5 – 1 = 8.3%
Effective semi-annual rate: = 4
Effective annual rate: 1.042 – 1 = 8.16%
b. Price of the bond = PV of coupons + PV of face value
PV of coupons = 25/ 0.04 x (1 – .04 10) = €202.77
PV of face value = .0410 = €675.56
Price of the bond = €878.33
The price is below the face value, because the APR is higher than the coupon rate
c. Same formula but with APR = 5
Price of the bond = €1000,- as the yield to maturity is now equal to the coupon rate
3
a. PV of a share =
PV of the coupons = 1..082 + .083 = €3.05
PV of the future stock price = .08 3 = €15.88
PV of a share = €18.93
b. Value of the share = .081 + .081 = €20.37
c. Price for a stock = 1..082 + .082 = €18.60
The price is higher, because the time is shorter, which means more security
1..082 + .083 = €18.92 or (20.37 + 1.70) / 1.082 = €18.92
At the second one you’re discounting the value you sell the stock for and the dividend you get
The value is the same as in question a (because?)
4
Value of a share: PV of the dividends in total
Timeline in notebook
PV first dividends = 0..06 + 0..06 2 + 1..063 + 1..064+ 1..065= €4.32
Year 1 until 5 the cashflows form a growing annuity; PV: 0.85 / (0.06 – 0.1) x (1 – (1.1/1.06) 5 =€4.32
PV horizon value = 1.28 / (0.06 – 0.03) = €42.67
From year 6 on, the cashflows form a growing perpetuity, which is delayed;
PV: 42..065 = €31.93
Value of a share = 42.67 + 4.32 = €46.99 31.93 + 4.32 = €36.25
a. One payment of coupon; 10% of €1000,- = €100,-
The payments are an annuity; .05 x (1 – .05 20) = €1246.22
b. PV of the bond = PV of the coupons + PV of the face value
PV of the bond = 1246.22 + .05 20 = 1246.22 + 376.89 = 1623.11
c. .0519 + .05 x (1 – .0519) + 100 = €1704.27
d. Answer c – 100 = €1604.27
2
a. The yield to maturity as an effective semi-annual rate is the same as the APR; 8%
The yield to maturity as an effective annual rate is (1 + 0..5) 0.5 – 1 = 8.3%
Effective semi-annual rate: = 4
Effective annual rate: 1.042 – 1 = 8.16%
b. Price of the bond = PV of coupons + PV of face value
PV of coupons = 25/ 0.04 x (1 – .04 10) = €202.77
PV of face value = .0410 = €675.56
Price of the bond = €878.33
The price is below the face value, because the APR is higher than the coupon rate
c. Same formula but with APR = 5
Price of the bond = €1000,- as the yield to maturity is now equal to the coupon rate
3
a. PV of a share =
PV of the coupons = 1..082 + .083 = €3.05
PV of the future stock price = .08 3 = €15.88
PV of a share = €18.93
b. Value of the share = .081 + .081 = €20.37
c. Price for a stock = 1..082 + .082 = €18.60
The price is higher, because the time is shorter, which means more security
1..082 + .083 = €18.92 or (20.37 + 1.70) / 1.082 = €18.92
At the second one you’re discounting the value you sell the stock for and the dividend you get
The value is the same as in question a (because?)
4
Value of a share: PV of the dividends in total
Timeline in notebook
PV first dividends = 0..06 + 0..06 2 + 1..063 + 1..064+ 1..065= €4.32
Year 1 until 5 the cashflows form a growing annuity; PV: 0.85 / (0.06 – 0.1) x (1 – (1.1/1.06) 5 =€4.32
PV horizon value = 1.28 / (0.06 – 0.03) = €42.67
From year 6 on, the cashflows form a growing perpetuity, which is delayed;
PV: 42..065 = €31.93
Value of a share = 42.67 + 4.32 = €46.99 31.93 + 4.32 = €36.25
