When purchasing the rights to a royalty, depending on the seller’s desired cash flows, Royalty Pharma can provide different types of payment schedules, such as an accelerated royalty or a synthetic royalty. In an accelerated royalty investment, Royalty Pharma provides the seller with the cash flow from a royalty over a shorter duration than the actual royalty.
For example, suppose the seller agrees to receive a fixed annual payment from Royalty Pharma for three years instead of 3% royalty on net sales over the course of 9 years. Assuming net sales of $1 billion per year, and a discount rate of 10%, what is the minimum acceptable fixed annual payment for this three-year agreement? Assume all cash flows including royalties occur at the end of the year so the first payment is made in exactly 1 year. (Note: Your answer should be expressed in units of millions of dollars.)
I'm not sure how to start..How can I start working this out??
Anyone??
To start working out the problem, we need to calculate the present value of the cash flows for both scenarios - the accelerated royalty payment and the actual royalty payment.
In the accelerated royalty payment scenario, we need to find the fixed annual payment that Royalty Pharma needs to provide to the seller for three years. We know that the net sales per year are $1 billion, and the discount rate is 10%.
To calculate the present value of cash flows for the accelerated royalty payment scenario, we can use the formula for the present value of an annuity:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
PMT = Fixed annual payment
r = Discount rate
n = Number of years
In this case, PV is the value we need to calculate, PMT is what we're trying to determine, r is 10%, and n is 3 years.
Let's plug the values into the formula and solve for PMT:
PV = PMT * [1 - (1 + 0.10)^(-3)] / 0.10
Now we need to solve for PMT.
To solve this problem, you need to calculate the present value of the cash flows from the accelerated royalty investment. Here's how you can start:
1. Determine the annual payment under the accelerated royalty agreement:
In this case, the seller agrees to receive a fixed annual payment for three years. Let's call this payment "P". To find the minimum acceptable fixed annual payment, we need to solve for P.
2. Calculate the present value of the cash flows from the accelerated royalty investment:
The present value (PV) of a future cash flow is the value of that cash flow today, taking into account the time value of money. To calculate the present value, we will discount each future cash flow back to the present using the given discount rate.
The net sales for each year are $1 billion. Since the royalty rate is 3%, the royalty payment for each year would be 3% of $1 billion, or $30 million. However, under the accelerated royalty agreement, the seller receives a fixed payment instead of the full royalty.
So, for year 1, the present value of the payment is P / (1 + 0.1)^1 (since it occurs at the end of year 1).
For year 2, the present value of the payment is P / (1 + 0.1)^2 (since it occurs at the end of year 2).
For year 3, the present value of the payment is P / (1 + 0.1)^3 (since it occurs at the end of year 3).
3. Set up the equation for the present value of the cash flows:
We'll sum up the present values of the cash flows and set it equal to the present value of the discounted royalties over the same time period.
P / (1 + 0.1)^1 + P / (1 + 0.1)^2 + P / (1 + 0.1)^3 = (0.03 * $1 billion) / (1 + 0.1)^1 + (0.03 * $1 billion) / (1 + 0.1)^2 + (0.03 * $1 billion) / (1 + 0.1)^3
4. Solve the equation for P:
Now, you can solve the equation numerically to find the value of P. You can use a calculator or software that supports numerical calculations, such as Excel or Google Sheets, to solve it.
Iterate through different values of P until you find the one that satisfies the equation. Start with a reasonable initial guess for P, and adjust it up or down based on the result of the equation. Repeat this process until you find a value for P that satisfies the equation.
Once you find the value of P, multiply it by $1 million to convert it to dollars.
That's how you can start working on this problem. The next steps involve solving the equation and calculating the minimum acceptable fixed annual payment for the three-year agreement.