Question

Solve in Excel

You are offered an investment with the following conditions:

• The cost of the investment is 1,000
• The investment pays out a sum X at the end of the first year; this payout grows at the rate of 10% per year for 11 years.

If your discount rate is 15%, calculate the smallest X which would entice you to purchase the asset.

Answer 1

Cost = PV of the payouts  
1000 = X/(1+15%) + X*(1+10%)/(1+15%)² .......+ X*(1+10%)¹¹/(1+15%)¹²
1000= X/1.15 (1 + 1.1/1.5 + (1.1/1.5)² ....+ (1.1/1.15)¹⁰
1000 = X/1.15 *(1-(1.1/1.15)¹¹/(1-1.1/1.5)
X = 1150/(1-(1.1/1.15)¹¹/(1-1.1/1.5) = 1150/7.734838 = 148.68

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