As Part Of A Business Combination, Mother Ryan Company Acqui
As Part Of A Business Combination Mother Ryan Company Acquired A Cust
As part of a business combination, Mother Ryan company acquired a customer list and a franchise agreement. Mother Ryan uses the expected cash flow approach for estimating the fair value of these two intangibles. The appropriate interest rate is 8%. The potential future cash flows from the two intangibles, and their associated probabilities, are as follows:
Customer List
- Outcome 1: 17% probability of cash flows of $40,000 at the end of each year for five years
- Outcome 2: 29% probability of cash flows of $18,000 at the end of each year for four years
- Outcome 3: 54% probability of cash flows of $9,000 at the end of each year for three years
Franchise Agreement
- Outcome 1: 15% probability of cash flows of $450,000 at the end of each year for 10 years
- Outcome 2: 19% probability of cash flows of $12,000 at the end of each year for four years
- Outcome 3: 66% probability of cash flows of $500 at the end of each year for three years
Using the expected cash flow approach, estimate the fair value of the customer list and of the franchise agreement. Round your calculations to the nearest whole dollar. Total estimated fair value of the customer list $______________ Total estimated fair value of the franchise agreement $________________
Paper For Above instruction
The valuation of intangible assets such as customer lists and franchise agreements is critical in the context of business acquisitions and mergers. Accurate valuation not only influences the purchase price but also impacts subsequent accounting, reporting, and strategic decision-making. This paper employs the expected cash flow approach, incorporating probabilistic outcomes and discounting future cash flows at an 8% interest rate to estimate the fair values of these assets, as instructed.
Valuation Methodology
The expected cash flow approach involves calculating the weighted average of possible future cash flows, where each outcome's probability weighs the respective cash flow estimates. This approach aligns well with intangible assets that have variable future economic benefits depending on different scenarios, which are inherently uncertain. Discounting these expected cash flows at the appropriate rate accounts for the time value of money, revealing the present value that reflects market perceptions of risk and return.
Calculation of Fair Value of the Customer List
Each outcome is associated with a specific probability, cash flow stream, and duration. The calculation proceeds in two steps: first determining the present value (PV) of cash flows for each outcome, then obtaining the expected value weighted by the probability of each outcome.
The present value of a cash flow received at the end of year n is calculated as:
PV = Future Cash Flow / (1 + discount rate)^n
Applying this to each outcome:
Outcome 1: 17% probability, $40,000 annually for 5 years
- Year 1: $40,000 / (1.08)^1 ≈ $37,037
- Year 2: $40,000 / (1.08)^2 ≈ $34,298
- Year 3: $40,000 / (1.08)^3 ≈ $31,787
- Year 4: $40,000 / (1.08)^4 ≈ $29,393
- Year 5: $40,000 / (1.08)^5 ≈ $27,216
Total PV for Outcome 1 = sum of above ≈ $159,731
Outcome 2: 29% probability, $18,000 annually for 4 years
- Year 1: $18,000 / (1.08)^1 ≈ $16,667
- Year 2: $18,000 / (1.08)^2 ≈ $15,432
- Year 3: $18,000 / (1.08)^3 ≈ $14,287
- Year 4: $18,000 / (1.08)^4 ≈ $13,236
Total PV for Outcome 2 ≈ $59,622
Outcome 3: 54% probability, $9,000 annually for 3 years
- Year 1: $9,000 / (1.08)^1 ≈ $8,333
- Year 2: $9,000 / (1.08)^2 ≈ $7,716
- Year 3: $9,000 / (1.08)^3 ≈ $7,143
Total PV for Outcome 3 ≈ $23,193
The expected cash flow (ECF) is then calculated as:
ECF = (Probability 1 × PV 1) + (Probability 2 × PV 2) + (Probability 3 × PV 3)
Converting percentages to decimals and computing:
ECF = (0.17 × $159,731) + (0.29 × $59,622) + (0.54 × $23,193) ≈ $27,157 + $17,297 + $12,516 = $57,970
Thus, the estimated fair value of the customer list is approximately $57,970.
Calculation of Fair Value of the Franchise Agreement
The same methodology is applied to the franchise agreement, with its respective cash flows and probabilities.
Outcome 1: 15% probability, $450,000 annually for 10 years
- Calculations involve summing the present values of the annuity over 10 years, which can be simplified using the Present Value of Annuity formula:
PV of annuity = Cash Flow × [(1 - (1 + r)^-n) ) / r]
where r = 8%, n = 10, and Cash Flow = $450,000
PV = $450,000 × [(1 - (1 + 0.08)^-10) ) / 0.08] ≈ $450,000 × 6.7101 ≈ $3,019,545
Outcome 2: 19% probability, $12,000 annually for 4 years
- PV of annuity = $12,000 × [(1 - (1 + 0.08)^-4) ) / 0.08] ≈ $12,000 × 3.3121 ≈ $39,745
Outcome 3: 66% probability, $500 annually for 3 years
- PV of annuity = $500 × [(1 - (1 + 0.08)^-3) ) / 0.08] ≈ $500 × 2.5432 ≈ $1,272
Calculate the expected value:
ECF = (0.15 × $3,019,545) + (0.19 × $39,745) + (0.66 × $1,272) ≈ $452,932 + $7,552 + $839 = $461,323
Therefore, the estimated fair value of the franchise agreement is approximately $461,323.
Conclusion
Based on the calculations, the fair value of the customer list, considering the probabilistic outcomes and discounting for the time value, is approximately $57,970. For the franchise agreement, the estimated fair value is around $461,323. These valuations provide crucial insights for strategic decision-making, financial reporting, and investment considerations in the context of business combinations.
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