Independent solution

How to solve this Deferred Growing Perpetuity question

Setup

Setup

Split the cash-flow stream into its five level payments and the growing perpetuity that starts afterward. The valuation rate is 9.2% effective annually.

167.50=10a5‾∣ 0.092+10v5(1+k)/1.0921−(1+k)/1.092167.50=10a_{\overline5|\,0.092}+10v^5\frac{(1+k)/1.092}{1-(1+k)/1.092}

Model

Model

The first component is a five-payment annuity-immediate. At time 5, the remaining payments have a geometric present value with ratio (1 + k)/1.092, which is then discounted back five years.

128.8045=135.2445(1+k)/1.092128.8045=135.2445(1+k)/1.092

Compute

Compute

After subtracting the level-annuity value, the equation reduces to 128.8045 = 135.2445(1 + k)/1.092. Solving gives k = 0.0400, or 4.0%.

k=0.0400k=0.0400

Answer

Answer

The calculation gives 4.0 for deferred growing perpetuity, matching published choice A.

K=4.0%(A)\boxed{K=4.0\%\quad\text{(A)}}