Rierson owns a garment factory in Spain and sells designer clothes to US and other European countries. He is trying attract some investments from US that he can use to expand further into the US market. US investors are looking for stable cash flow, which is going to be a challenge given that the fashion industry is changing constantly and he can get stuck with unsold inventory. To allay their fears, Rierson decides to investment some of the capital raised into Italian 10 year Government Bonds. He explains that the return from these bonds will be used to improve his operations. Ignoring currency exposure, consider the following:
He decides to invest into ten year 1,000 EURO Government bond with 8% coupon rate and semi-annual coupons. If the bond is currently trading for a price of 957.35 Euros, what is the bond’s yield to maturity? Assume is buys 10,000 of these bonds.
Suppose he is told that the yield to maturity has increased to 15% (expressed as an APR with semiannual compounding). What price is the bond trading for now?
| YTM is the rate at which price of bond if discounted is = PV cashflows of bond | ||||
| Coupon = | 1000 x 8% x 1/2 = | 40 | ||
| No. of payments = | 10 x 2 = | 20 | ||
| Selling price = | 957.35 | |||
| 957.35 | = | 40 x PVAF(YTM,20) + 1000 x PVIF(YTM,20) | ||
| YTM | Price | |||
| 5% | 875.3779 | |||
| YTM | 957.35 | |||
| 4.0% | 1000 | |||
| Using linear Interpolation - | ||||
| YTM-4/5-4 = | 957.35-1000/875.3779-1000 | |||
| YTM-4 = | -42.65/-124.622 | |||
| YTM-4 = | 0.342235 | |||
| YTM = | 4.342235 | Semi annual | ||
| BEY = | 4.342235 x 2 = | 8.684469 | Annual | |
| IF YTM is 15% - | ||||
| Rate = | 15/2 = | 7.50 | ||
| Price = | 40 x PVAF(7.5%,20) + 1000 x PVIF(7.5%,20) | |||
| 40 x 10.19449 + 1000 x 0.23541 | ||||
| 643.1928 | ||||
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