Valuation of Bonds and Stocks
1. Lucky Industry purchased a 15-year, P1,000 face value bond pays interest of P37.50 every 3 months.
If you require a simple annual rate of return of 12 percent, with quarterly compounding, how much
should you be willing to pay for this bond?
Answer:
VB = FV(1+i)-n + CP 1-(1+i)-n
i
= P1,000(1.03)-60 + 37.50 1 – (1.03)-60
0.03
= P169.73 + P1,037.83
= P1,207.56
2. Lucky Industry purchased a 15-year, P1,000 face value bond pays interest of P37.50 every 6 months.
If you require a simple annual rate of return of 12 percent, with semi-annual compounding, how much
should you be willing to pay for this bond?
Answer:
VB = FV(1+i)-n + CP 1-(1+i)-n
i
= P1,000(1.06)-30 + 37.50 1 – (1.06)-30
0.06
= P174.11 + P516.18
= P690.29
3. The Banana Republic issued P50 million of government bonds in 2015. The bonds were issued in
P100 denominations with an annual coupon interest rate of 8%. Determine the current yield on these
bonds if they are purchased at the current price of P40.
Answer: Current yield = Coupon payment = 8 = 20.0%
Value of bond 40
4. In 2012, Swiss Corporation sold a P250 million bond issue to finance the purchase of new jet
airliners. These bonds were issued in P1000 denominations with an original maturity of 12 years and
a coupon rate of 12%. In 2014, determine the value of one of these bonds to an investor who requires
a 14% rate of return on these securities.
VB = FV(1+i)-n + CP 1-(1+i)-n
i
= P1,000(1.14)-10 + 120.00 1 – (1.14)-10
0.14
= P269.74 + P625.93
= P895.68
1
5. What is the value of a 15-year 10% coupon bond with a face value of P1,000. The required return on
the bond is 12% and the bond makes semiannual payments.
Answer: VB = 1,000(1.06)-30 + 50 1 – (1.06)-30
0.06
= P862.35
6. Sambokojin normally pays out 30% dividends from of its earnings. The previous year, earnings
available for common stockholders were P256 million. Sambokojin’s equity was P678 million. What
is the growth rate?
Answer: g = ROE(1 – DPO)
= 256 (1 - 0.30) = 26.43%
678
7. At the start of the year, the CEO of Buffet 101 is planning to purchase WEB stock and to hold it for 1
year. By the end of the year, the CEO is expecting to receive a dividend of P5.50 and to sell the stock
for P154. The required rate of return of WEB stock is 16 percent. How much should be the purchase
price of the stock?
Answer: P0 = (P5.50+P154) = P137.50
1.16
8. Fast Wheels, Inc. expects to pay an annual dividend of P0.72 next year. Dividends have been growing
at a compound annual rate of 6 percent and are expected to continue growing at that rate. What is the
value of a share of stock of Fast Wheels to an investor who requires a 14 percent rate of return?
Answer: P0 = P0.72/(0.14 - 0.06) = P9.00
9. What is the current value of the common stock of SCHP Corporation if you know the current
dividend yield is 6.14%, the PE is 16, and the annual dividend is P1.35?
Answer: Price = dividend/current yield = P1.35/0.0614 = P21.99
10. What is the current value of a share of Chyrox if its current dividend is P1.50 and dividends are
expected to grow at an annual rate of 20 percent for the next 5 years? Assume the investor has a
required rate of return of 15 percent and expects to sell the security in 5 years for P72.
Answer:
Year
1 P1.50(1.20) = 1.80(0.87) = P 1.57
2 P1.80(1.20) = 2.16(0.756) = 1.63
3 P2.16(1.20) = 2.59(0.658) = 1.70
4 P2.59(1.20) = 3.11(0.572) = 1.78
5 P3.11(1.20) = 3.73(0.497) = 1.85
P5= P72(0.497) = 35.78
P0 = P44.31
2
11. The earnings and dividends of Nebula Computer Co. are expected to grow at an annual rate of 15
percent over the next 4 years and then slow to a constant growth rate of 8 percent per year. Nebula
currently pays a dividend of P0.50 per share. What is the value of Nebula stock to an investor who
requires a 14 percent rate of return?
Answer:
Year
1 P0.50(1.15) = 0.575(.877) = P0.504
2 P0.575(1.15) = 0.661(.769)= .509
3 P0.661(1.15) = 0.760(.675)= .513
4 P0.760(1.15) = 0.874(.592)= .518
= P2.04
P4 = P0.874(1.08)/(0.14 - 0.08) = P15.73(0.592) = 9.31
P0 = P11.35
12. Snackoo, Inc. bonds currently sell for P1,100. They pay a P90 annual coupon, have a 25-year
maturity, and a P1,000 par value, but they can be called in 5 years at P1,050. Assume that no costs
other than the call premium would be incurred to call and refund the bonds, and also assume that the
yield curve is horizontal, with rates expected to remain at current levels on into the future. What is
the difference between this bond's YTM and its YTC?
AYTM = 90 + (P1,000 – P1,100)
25
P1,000(0.40) + P1,100(0.60)
= 0.0811 or 8.11%
AYTC = 90 + (P1,050 – P1,100)
5
P1,000(0.40) + P1,100(0.60)
= 0.0755 or 7.55%
Difference = 8.11% - 7.55%
= 0.56%
