Question

Camden’s Antiques, Inc. just added a whole new line of furniture to his product line. Camden expects this addition to result in record high dividends of $3.15 and $4.15 in the next two years. After that, he thinks his growth will level off at its usual 3% rate. The rate expected in the marketplace for investments similar to Camden’s is 5%.

What is the current value of a share of Camden’s?

What will the value of a share be in year two (P2)?

What will the value of a share be in year thirteen (P13)?

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Max is thinking about buying a $1,000 bond that has a 5% semiannual coupon and 12 years to maturity. The expected rate in the marketplace for investments similar to this is 7.5%.

Will this bond be a premium or discount bond? __________________

What is the present value of the coupon stream? ________________

What is the present value of the face value? ____________________

What is the total value of the bond? ___________________________

If the bond is priced at 98, should Max buy or not buy? ___________

Answer 1

Answer to Question 1:

Part a:

Dividend in Year 1, D1 = $3.15
Dividend in Year 2, D2 = $4.15

Growth Rate, g = 3%
Expected Return, rs = 5%

Dividend in Year 3, D3 = D2 * (1 + g)
Dividend in Year 3, D3 = $4.15 * 1.03
Dividend in Year 3, D3 = $4.2745

Value of Share in Year 2, P2 = D3 / (rs - g)
Value of Share in Year 2, P2 = $4.2745 / (0.05 - 0.03)
Value of Share in Year 2, P2 = $4.2745 / 0.02
Value of Share in Year 2, P2 = $213.725

Current Value of Share, P0 = $3.15/1.05 + $4.15/1.05^2 + $213.725/1.05^2
Current Value of Share, P0 = $200.62

Part b:

Value of Share in Year 2, P2 = $213.725

Part c:

Dividend in Year 14, D14 = D2 * (1 + g)^12
Dividend in Year 14, D14 = $4.15 * 1.03^12
Dividend in Year 14, D14 = $5.9169

Value of Share in Year 13, P13 = D14 / (rs - g)
Value of Share in Year 13, P13 = $5.9169 / (0.05 - 0.03)
Value of Share in Year 13, P13 = $5.9169 / 0.02
Value of Share in Year 13, P13 = $295.85

Answer to Question 2:

Part a:

Market interest rate is higher than stated interest rate; therefore, this bond will trade at a discount.

Part b:

Face Value = $1,000

Annual Coupon Rate = 5.00%
Semiannual Coupon Rate = 2.50%
Semiannual Coupon = 2.50% * $1,000
Semiannual Coupon = $25

Time to Maturity = 12 years
Semiannual Period = 24

Annual Interest Rate = 7.50%
Semiannual Interest Rate = 3.75%

Present Value of Coupon Stream = $25/1.0375 + $25/1.0375^2 + … + $25/1.0375^23 + $25/1.0375^24
Present Value of Coupon Stream = $25 * (1 - (1/1.0375)^24) / 0.0375
Present Value of Coupon Stream = $25 * 15.644824
Present Value of Coupon Stream = $391.12

Part c:

Present Value of Face Value = $1,000/1.0375^24
Present Value of Face Value = $413.32

Part d:

Total Value of Bond = Present Value of Coupon Stream + Present Value of Face Value
Total Value of Bond = $391.12 + $413.32
Total Value of Bond = $804.44

Part e:

Quoted Price = 98

Market Price = 98% * $1,000
Market Price = $980

Market price is higher than value of bond; therefore, Max should not buy this bond.