Final answer:
To determine the present value of a 15-year investment with a growing first payment and a specific discount rate, apply the present value formula to each payment, adjusting each for growth, and then sum the present values.
Step-by-step explanation:
The question involves calculating the present value of a 15 year investment with a first payment of £150,000 that grows at a rate of 3.75% each year, using a discount rate of 8%. To find the present value, we need to discount each of the annual payments back to their value at the present time considering the growth rate of the payments and the given discount rate. This requires the application of the present value formula for each year and then summing them all up to get the total present value of the investment.
The present value (PV) of a single future payment is calculated using the formula PV = FV / (1 + r)^n where FV represents the future value of the payment, r is the discount rate, and n represents the number of years until the payment is received. The payments grow each year, so each payment needs to be calculated separately taking the growth into account and then discounted back to present value using the formula above for each year.