Arrange (in descending order) the following present value of a growing perpetuity which makes first payment of ₹3,000 in next year.

A. Present value at 8% growth and 10% discount rate.
B. Present value at 3% growth and 9% discount rate.
C. Present value at 6% growth and 11% discount rate.
D. Present value at 5% growth and 6% discount rate.
E. Present value at 1% growth and 4% discount rate.

Choose the correct answer from the options given below:

Correct option is C

To calculate the present value of a growing perpetuity, we use the formula:

Where:
C = First payment = ₹3,000
r = Discount rate
g = Growth rate

Now, calculate each:

A → PV = 3000 / (0.10 - 0.08) = ₹1,50,000
B → PV = 3000 / (0.09 - 0.03) = ₹50,000
C → PV = 3000 / (0.11 - 0.06) = ₹60,000
D → PV = 3000 / (0.06 - 0.05) = ₹3,00,000
E → PV = 3000 / (0.04 - 0.01) = ₹1,00,000

Now arranging in descending order:
D = ₹3,00,000
A = ₹1,50,000
E = ₹1,00,000
C = ₹60,000
B = ₹50,000

So, the correct order is D, A, E, C, B.

Information Booster:

• The smaller the difference between discount rate (r) and growth rate (g), the larger the PV.

• In D, (r - g) = 1%, so PV = ₹3,00,000 (the highest).

• A and E have closer gaps than B and C, so they rank next.

• This formula assumes perpetual and growing cash flows, starting one year from now.

• Present Value increases non-linearly as (r - g) becomes smaller.

• Applicable only when r > g; otherwise, the formula becomes invalid or infinite.