Customer Acquisition costs were calculated at $472,000 to be spent in 2021 to acquire 250 new customers.

These customers will have a 3 year customer lifetime value and the net cash benefits per year are estimated as follows:

Year 1 $157,000
Year 2 $221,000
Year 3 $177,000

The discount rate is 11%

What is the closest proximate of lifetime value (benefit or erosion) resulting from this customer acquisition investment over the lifecycle?

Question

Customer Acquisition costs were calculated at $472,000 to be spent in 2021 to acquire 250 new customers.

These customers will have a 3 year customer lifetime value and the net cash benefits per year are estimated as follows:

Year 1  $157,000
Year 2  $221,000
Year 3  $177,000

The discount rate is 11%

What is the closest proximate of lifetime value (benefit or erosion) resulting from this customer acquisition investment over the lifecycle?

BlackTom AI · Accepted Answer

To evaluate the lifetime value (LTV) of the customer acquisition investment, we start by determining the present value of the expected cash benefits over the three-year horizon and then subtract the acquisition cost.

First, compute the present value (PV) of Year 1 benefits. With a discount rate of 11%, the discount factor is 1/1.11 ≈ 0.9009. So PV of Year 1 benefits = 157,000 × 0.9009 ≈ 141,441.

Next, compute the PV of Year 2 benefits. The discount factor for two years is 1/(1.11)^2 ≈ 1/1.2321 ≈ 0.8116. Thus PV of Year 2 benefits = 221,000 × 0.8116 ≈ 179,396.

Then, compute the PV of Year 3 benefits. The discount factor for three years is 1/(1.11)^3 ≈ 1/1.367631 ≈ 0.7310. So PV of Year 3 benefits = 177,000 × 0.7310 ≈ 129,387.

Now sum the present values of all three years to obtain the total PV of benefits: 141,441 + 179,396 + 129,387 ≈ 450,224.

Subtract the acquisition cost to get the net lifetime value: 450,224 − 472,000 ≈ −21,776. In other words, the investment would erode value by roughly $21.8k over the three-year lifecycle.

To interpret variations and potential rounding, note that small differences in discounting precision (e.g., using 0.9009 vs 0.900) can shift the final figure slightly, but the result remains a negative net present value, indicating erosion rather than value creation for this cohort over three years.

2025FA_IMC_402-0_SEC20 Practice Exam for Final

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