Practice Question
"Joey, Connor, and Grant are thinking about selling their podcast's media rights to Fuji TV (フジテレビ). The Japanese television network offered a particular deal, and it goes as follows. They're going to be paid $99.97 in 3 year(s) from now, and these initial cash flows will grow by 28.10% per year for 2 years. However, the growth rate will fall to a fixed 6.95% thereafter. Note that Joey, Connor, and Grant's required rate of return is 14.07%. What is the present value of this deal? And, should they accept this deal if they were offered a $430 lump sum payment by a competing Japanese television network?"
Select the closest answer: $1,186.83, $1,278.21, $1,342.12, $1,374.07, $1,207.91
Step 1: Highlight Relevant Information & Define Key Variables
PMT = $99.97
k = 14.07%
g₁ = 28.10% (for 2 years)
g₂ = 6.95% (in perpetuity)
Note: First payment starts in year 3, growth lasts until year 5, then perpetuity begins
Step 2: Build the Timeline
Separate the problem into two sections: a growing annuity (years 3 to 5), and a growing perpetuity starting from year 6. We'll compute each present value separately, then discount both back to t = 0.
Step 3: Solve for the Growing Annuity (Years 3–5)
Using the formula:
PV₂ = PMT₃ × [(1 - ((1 + g₁)/(1 + k))ⁿ) / (k - g₁)]
PV₂ = 99.97 × [(1 - ((1 + 0.2810)/(1 + 0.1407))²) / (0.1407 - 0.2810)]
PV₂ ≈ $186.06
Now discount back to time 0:
PV₀ = PV₂ / (1 + k)² = 186.06 / (1.1407)² ≈ $142.99
Step 4: Solve for the Growing Perpetuity (Starting Year 6)
PMT₅ = PMT₃ × (1 + g₁)² = 99.97 × (1.2810)² ≈ $163.94
PMT₆ = PMT₅ × (1 + g₂) = 163.94 × 1.0695 ≈ $175.34
PV₄ = PMT₆ / (k - g₂) = 175.34 / (0.1407 - 0.0695) ≈ $1,922.10
Now discount to time 0:
PV₀ = 1922.10 / (1.1407)⁴ ≈ $1,135.22
Step 5: Add Both Components
Total PV₀ = $142.99 + $1,135.22 = $1,278.21
Conclusion:
Since $1,278.21 > $430, Joey, Connor, and Grant should accept the Fuji TV offer.