You Wrote A Piece Of Software That Does A Better Job Of Allo
You Wrote A Piece Of Software That Does A Better Job Of Allowing Compu
You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into their systems and is offering to pay you $503,000 today, plus $503,000 at the end of each of the following six years for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you?
Paper For Above instruction
The present value (PV) of a series of cash flows is a fundamental concept in finance, representing the current worth of a stream of future payments discounted at a specific interest rate. In this case, the cash flow stream consists of an immediate payment and a series of annual payments over six years, with an interest rate of 6 percent. Calculating this PV involves discounting both the lump-sum payment received immediately and the annuity of subsequent payments to their present values.
Initially, the immediate payment of $503,000 received today is straightforward; its present value equals its face value. The more complex part involves calculating the present value of the annuity—each of the six payments of $503,000 occurring at the end of each year from year one through year six. This process involves applying the present value of an annuity formula:
PV of Annuity = P × [(1 - (1 + r)^-n) / r]
where:
- P is the payment per period ($503,000),
- r is the interest rate per period (6% or 0.06),
- n is the total number of periods (6 years).
Calculating the present value involves two steps: first, computing the PV of the future payments, and then adding the immediate payment.
The PV of the future payments becomes:
PV of annuity = $503,000 × [(1 - (1 + 0.06)^-6) / 0.06]
Calculating the discount factor for 6 years:
(1 + 0.06)^6 ≈ 1.418519
Taking the inverse:
(1 + 0.06)^-6 ≈ 1 / 1.418519 ≈ 0.704
Thus, the annuity factor is:
(1 - 0.704) / 0.06 ≈ 0.296 / 0.06 ≈ 4.933
Multiplying by the payment:
PV of annuity ≈ $503,000 × 4.933 ≈ $2,479,099
Adding the immediate payment of $503,000:
Total present value = $503,000 + $2,479,099 ≈ $2,982,099
Therefore, the total present value of the cash flow stream offered by the company is approximately $2,982,099 when discounted at a 6 percent interest rate. This calculation illustrates how future cash flows are valued today and helps inform financial decisions regarding licensing and negotiations in technology transactions. Proper valuation ensures that expected future earnings are correctly accounted for in present terms, a critical aspect of financial management in technological innovations.
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