TUTORIAL QUESTIONS
Asset Valuation
1. Callaghan Motor’s bonds have 10 years remaining to maturity. Interest is paid annually, the
bonds have a $1,000 par value, and the coupon rate is 8%. The bonds have a yield to maturity
of 9%. What is the current market price of these bonds?
𝑉𝑏=80 (𝑃𝑉𝐼𝐹𝐴9%,10) + 1,000 (𝑃𝑉𝐼𝐹9%,10)
𝑉𝑏=80 (6.4176) + 1,000 (0.4224)
𝑉𝑏=513.41+ 422.4
𝑉𝑏=𝟗𝟑𝟓.𝟖𝟏
2. Nungesser Corporation has issued bonds that have a 9% coupon rate, payable semi-annually.
The bonds mature in 8 years, have a face value of $1,000, yield to maturity of 8.5%. What is
the price of the bonds?
𝑉𝑏 = 45 (𝑃𝑉𝐼𝐹𝐴4.25%,16) + 1,000 (𝑃𝑉𝐼𝐹4.25%,16)
𝑉𝑏=45 〔(45) 〕〔1 − 1____ 〕
(1+ 0.0425)16
0.0425 + 1,000(1/1+0.0425)16
𝑉𝑏=45 11.4403 + 1,000 0.5138
𝑉𝑏=514.81+ 513.80
𝑉𝑏=𝟏,𝟎𝟐𝟖.𝟔𝟏
3. Wilson Wonder’s bonds have 12 years remaining to maturity. Interest is paid annually, the
bonds have a $1,000 par value, and the coupon rate is 10%. The bonds sell at a price of $850.
What is the yield to maturity?
𝑌𝑇𝑀=𝑌𝑖𝑒𝑙𝑑 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑛𝑑
𝐼=𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡= 1,000 (0.10) =100
𝑀=𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒=1,000
𝑃0=𝑃𝑟𝑖𝑐𝑒=850
𝑛=𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦=12
𝑌𝑇𝑀= 100 + 1,000− 850_
12____
1,000 + 850
2
𝑌𝑇𝑀= 100 + 12.50
1
, 925
𝑌𝑇𝑀=0.1216
𝒀𝑻𝑴=𝟏𝟐.𝟏𝟔%
4. The Pennington Corporation issued a new series of bonds on January 1, 1979. The bonds were
sold at par ($1,000), have a 12 percent coupon, and mature in 30 years, on December 31, 2008.
Coupon payments are made semiannually (on June 30 and December 31).
a. What was the YTM of Pennington’s bonds on January 1, 1979?
b. What was the price of the bond on January 1, 1984, 5 years later, assuming that the level of
interest rates had fallen to 10 percent?
c. On July 1, 2002, Pennington’s bonds sold for $916.42. What was the YTM at that date?
The Yield to Maturity, YTM of the bond is given by:
Where:
𝑌𝑇𝑀=𝑌𝑖𝑒𝑙𝑑 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑛𝑑
𝐼=𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑀=𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒
𝑃0=𝑃𝑟𝑖𝑐𝑒
𝑛=𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦
(a) The Yield to Maturity on January 1, 1979 was 12% since the bond was issued at Par
(b)
𝑉𝑏 = 60 𝑃𝑉𝐼𝐹𝐴10%,50 + 1,000 𝑃𝑉𝐼𝐹10%,50
𝑉𝑏 = 60 (18.256) + 1,000 (0.0872)
𝑉𝑏 = 1,095.36 + 87.20
𝑉𝑏 = 𝟏,𝟏𝟖𝟐.𝟓𝟔
(c)
2
Asset Valuation
1. Callaghan Motor’s bonds have 10 years remaining to maturity. Interest is paid annually, the
bonds have a $1,000 par value, and the coupon rate is 8%. The bonds have a yield to maturity
of 9%. What is the current market price of these bonds?
𝑉𝑏=80 (𝑃𝑉𝐼𝐹𝐴9%,10) + 1,000 (𝑃𝑉𝐼𝐹9%,10)
𝑉𝑏=80 (6.4176) + 1,000 (0.4224)
𝑉𝑏=513.41+ 422.4
𝑉𝑏=𝟗𝟑𝟓.𝟖𝟏
2. Nungesser Corporation has issued bonds that have a 9% coupon rate, payable semi-annually.
The bonds mature in 8 years, have a face value of $1,000, yield to maturity of 8.5%. What is
the price of the bonds?
𝑉𝑏 = 45 (𝑃𝑉𝐼𝐹𝐴4.25%,16) + 1,000 (𝑃𝑉𝐼𝐹4.25%,16)
𝑉𝑏=45 〔(45) 〕〔1 − 1____ 〕
(1+ 0.0425)16
0.0425 + 1,000(1/1+0.0425)16
𝑉𝑏=45 11.4403 + 1,000 0.5138
𝑉𝑏=514.81+ 513.80
𝑉𝑏=𝟏,𝟎𝟐𝟖.𝟔𝟏
3. Wilson Wonder’s bonds have 12 years remaining to maturity. Interest is paid annually, the
bonds have a $1,000 par value, and the coupon rate is 10%. The bonds sell at a price of $850.
What is the yield to maturity?
𝑌𝑇𝑀=𝑌𝑖𝑒𝑙𝑑 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑛𝑑
𝐼=𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡= 1,000 (0.10) =100
𝑀=𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒=1,000
𝑃0=𝑃𝑟𝑖𝑐𝑒=850
𝑛=𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦=12
𝑌𝑇𝑀= 100 + 1,000− 850_
12____
1,000 + 850
2
𝑌𝑇𝑀= 100 + 12.50
1
, 925
𝑌𝑇𝑀=0.1216
𝒀𝑻𝑴=𝟏𝟐.𝟏𝟔%
4. The Pennington Corporation issued a new series of bonds on January 1, 1979. The bonds were
sold at par ($1,000), have a 12 percent coupon, and mature in 30 years, on December 31, 2008.
Coupon payments are made semiannually (on June 30 and December 31).
a. What was the YTM of Pennington’s bonds on January 1, 1979?
b. What was the price of the bond on January 1, 1984, 5 years later, assuming that the level of
interest rates had fallen to 10 percent?
c. On July 1, 2002, Pennington’s bonds sold for $916.42. What was the YTM at that date?
The Yield to Maturity, YTM of the bond is given by:
Where:
𝑌𝑇𝑀=𝑌𝑖𝑒𝑙𝑑 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑛𝑑
𝐼=𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡
𝑀=𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒
𝑃0=𝑃𝑟𝑖𝑐𝑒
𝑛=𝑌𝑒𝑎𝑟𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦
(a) The Yield to Maturity on January 1, 1979 was 12% since the bond was issued at Par
(b)
𝑉𝑏 = 60 𝑃𝑉𝐼𝐹𝐴10%,50 + 1,000 𝑃𝑉𝐼𝐹10%,50
𝑉𝑏 = 60 (18.256) + 1,000 (0.0872)
𝑉𝑏 = 1,095.36 + 87.20
𝑉𝑏 = 𝟏,𝟏𝟖𝟐.𝟓𝟔
(c)
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