David N.

asked • 04/30/20

Corporate Finance

In April 2014, Greece managed to sell some €3 billion in new five-year bonds at a yield of just 4.95%.

Answer the following questions (show all calculations):

Suppose a coupon of 4.75% (assume that each bond pays interest annually) and the actual yield to maturity (YTM) of 4.95%.


Suppose that an investor holds the bond of the above question for two years expecting that by the end of this period the YTM will have dropped to 2.6%, which was the YTM of the Portuguese sovereign debt of the same maturity in April 2014. What is the anticipated return of the investment (to calculate the overall profit you should take into consideration both the capital gains from the fall in the YTM and the coupons that have been paid)?


John L.

My two cents: In April 2014 Greece sold its 5-year 4.75% annual coupon bonds at a discount since market YTM of 4.95% is higher than the coupon rate of 4.75%. Greece sold these bonds as % of 100 par value of 99.1329066 or 2,973,987,196.72 in Euro terms. Bond value formula is 0.0475 * ( 1 - (1+0.0495)^(-5))/0.0495 + 1 /(1+0.0495)^5 Two years later, the investors expect the YTM on a Greece 3-year bond to be at 2.60%. With coupon rate being higher than YTM now, the bond will be trading in the market at premium to 100 par value of 106.1285871 or 3,183,857,613.43. To calculate the internal rate of return (expected total return on this investment over the two years investment horizon), we have the following inputs: Initial investment of 2,973,987,196.72. Coupon income of 142,500,000.00 in at end of year one and year two Selling the bond for 3,183,857,613.43 at the end of year two. Using Excel IRR function, we can compute an IRR of 8.18131831640891%. We can verify this number by setting up the following equation: 2,973,987,196.72 = 142,500,000.00 / ( 1 + 8.18131831640891% ) + ( 142,500,000.00 + 3,183,857,613.43 ) / ( 1 + 8.18131831640891% )^2 Note that in general there is "rolling down" the yield curve with a normal upward-sloping yield curve, as the bond's remaining term shortens as its gets closer to maturity. In this case, the investor buys at 5-year bond (with a YTM associated with 5 years) but sells it two years later as a 3-year bond (with a YTM associated with 3 years, which tends to be lower in an upward sloping yield curve)
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12/06/20

1 Expert Answer

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Nima N. answered • 04/30/20

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Hi David,


To answer this question, first calculate how much profit is gained from the coupon and the capital gains for the fall in the YTM. To note, when a bonds price increases, the yield will fall correspondingly.


Coupon Profit

€3,000,000,000 * (.0475) = 142,500,000 (coupon paid annually)

142,500,000 * 2 = 285,000,000 (because two years of coupons)


Calculate New Price of Bonds

Use the bond price formula

= (1 - (1 + .026/3)^(-.026*3))/(.026/3) + (3000000000)/((1+.026/3)^(-.026*3)) = 3,002,019,940 (new price of bond)


Total Profit

Capital Gains = 3,002,019,940 - 3,000,000,000 = 2,019,940

Coupon Gains = 285,000,000

Profit = 2,019,940 + 285,000,000 = 287,019,940

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John L.

My two cents: In April 2014 Greece sold its 5-year 4.75% annual coupon bonds at a discount since market YTM of 4.95% is higher than the coupon rate of 4.75%. Greece sold these bonds as % of 100 par value of 99.1329066 or 2,973,987,196.72 in Euro terms. Bond value formula is 0.0475 * ( 1 - (1+0.0495)^(-5))/0.0495 + 1 /(1+0.0495)^5 Two years later, the investors expect the YTM on a Greece 3-year bond to be at 2.60%. With coupon rate being higher than YTM now, the bond will be trading in the market at premium to 100 par value of 106.1285871 or 3,183,857,613.43. To calculate the internal rate of return (expected total return on this investment over the two years investment horizon), we have the following inputs: Initial investment of 2,973,987,196.72. Coupon income of 142,500,000.00 in at end of year one and year two Selling the bond for 3,183,857,613.43 at the end of year two. Using Excel IRR function, we can compute an IRR of 8.18131831640891%. We can verify this number by setting up the following equation: 2,973,987,196.72 = 142,500,000.00 / ( 1 + 8.18131831640891% ) + ( 142,500,000.00 + 3,183,857,613.43 ) / ( 1 + 8.18131831640891% )^2 Note that in general there is "rolling down" the yield curve with a normal upward-sloping yield curve, as the bond's remaining term shortens as its gets closer to maturity. In this case, the investor buys at 5-year bond (with a YTM associated with 5 years) but sells it two years later as a 3-year bond (with a YTM associated with 3 years, which tends to be lower in an upward sloping yield curve)
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12/06/20

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