Independent solution

How to solve this Reinvestment Scenario Analysis question

Setup

Setup

The bond’s annual coupon is 5% of 822,703, or 41,135. Evaluate the investor’s terminal wealth separately under the two coupon-reinvestment rates.

C=822703(0.05)=41135C=822703(0.05)=41135

Model

Model

For each scenario, accumulate the four coupons with the appropriate annuity factor, add redemption, and subtract the 1,000,000 target amount.

ΠA=822703+41135s4‾∣ 0.045−1000000=−1313\Pi_A=822703+41135s_{\overline4|\,0.045}-1000000=-1313

Compute

Compute

The 4.5% scenario gives a loss of about 1,313, while the 5.5% scenario gives a gain of about 1,324. Rounded to the alternatives, the ordered pair is (−1,310, 1,320).

ΠB=822703+41135s4‾∣ 0.055−1000000=1324\Pi_B=822703+41135s_{\overline4|\,0.055}-1000000=1324

Answer

Answer

The calculation gives the statement identified by the conditions above for reinvestment scenario analysis, matching published choice D.

(−1310, 1320)(D)\boxed{(-1310,\ 1320)\quad\text{(D)}}