I have a case study to do and I'm not sure how to go about it. I need to find the present value for three different offers, all of which have a 10% rate and ordinary annuities. This is the first offer:
$1,000,000 now
$200,000 each year for years 6 through and including year 15
Also, if the product did over $100 million in cumulative sales by the end of year 15, he would receive an additional $3,000,000 at that time. Dr. Wolf thought there was a 70 percent probability this would happen.
So my question is how do I even begin calculating the present value, cause to do that I need the future value and I'm not sure how to get that either. Any help would be appreciated. Thank you.
To calculate the present value of an offer, you need to determine the future value of each cash flow and then discount those values back to the present using the given interest rate. Let's break down the calculations step by step for the first offer:
1. $1,000,000 now:
Since this amount is already available in the present, its present value is equivalent to its future value. Therefore, the present value of $1,000,000 is $1,000,000.
2. $200,000 each year for years 6 through 15:
To calculate the future value of this cash flow, you need to determine the value of the annuity for 10 years with an annual payment of $200,000. You can use the formula for the future value of an ordinary annuity:
Future Value = Payment × [(1 + Interest Rate) ^ Number of Periods - 1] / Interest Rate
In this case, the payment is $200,000, the interest rate is 10%, and the number of periods is 10 (years 6 through 15). Plugging these values into the formula, you can calculate the future value of this cash flow.
3. Additional $3,000,000 if cumulative sales exceed $100 million by year 15:
Since there is a 70% probability of this additional amount being received, we need to calculate the present value of $3,000,000 multiplied by the probability (0.70) to account for the uncertainty.
Finally, you can add up the present values of all three cash flows to obtain the total present value of the offer.
Remember that the future value calculations depend on the specific terms of the offer, such as the timing and amounts of payments. The formulas I mentioned here are general formulas for annuities, but the specific details of the offer will determine the correct values to use.
Good luck with your case study!