The Brady Plan,named after the American Secretary of the Treasury, include two m

Question

The Brady Plan,named after the American Secretary of the Treasury, include two methods for developing countries to reduce outstanding debt by replacing loans with bonds.
method A: replace loans with 30 years discount bonds that pay coupon once a year at a rate of 6.25%. The face value of the bonds would equal the outstanding debt on the loan being replaced.
method B: replace loans with 30 yr bonds selling at par that pay coupon once a year at a rate tied to the market. the face value of the bonds would equal 65% of the loans being replaced, the remaining 35% being forgiven
the bonds of method A and B would have the same yield to maturity, determine the approx yield to maturity that would equate the present value of payments under the two methods

Explanation / Answer

Let D be outstanding amount, yield be k and r be market rate For method A : PV(A) = D = D*0.0625 *((1+k)^30 -1)/(k(1+k)^30) For method B : PV(B) = D = 0.65D*r *((1+k)^30 -1)/(k(1+k)^30) PV(A) = PV(B) => D*0.0625 *((1+k)^30 -1)/(k(1+k)^30) =0.65 D*r*((1+k)^30 -1)/(k(1+k)^30) =>0.0625 = 0.65r =>r = 0.096 = 9.6% From PV(A), D = D*0.0625 *((1+k)^30 -1)/(k(1+k)^30) => 0.0625 *((1+k)^30 -1)/(k(1+k)^30) = 1 At k = 0,045, LHS = 1.018 = almost LHS Hence, k = 0.045 = 4.5% (ANSWER)

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