Hello and welcome. In this webcast, we will discuss the option to invest in an R&D project. In this example, we will go through a simple net present value analysis. From there, we will continue to a real options valuation. Consider a car manufacturer that is contemplating to develop a new type of electric car. The company has the following expected cash flows. During the two-year R&D phase, the project has expected cash outflows of minus 20 and minus 100. Following the R&D phase, is the commercialization phase. To start the commercialization phase, management has to invest another 1,600. Cash inflows are expected during the last four years of the project. Notice, that the R&D project consists of multiple stages. Immediate cash flows are required, while cash inflows are expected at a later point in time. In this example, we will assume that the risk-free rate is two percent, and that the opportunity cost of capital is equal to 16 percent. We further assume that cash outflows are discounted with a risk-free rate and that cash inflows are discounted with the opportunity cost of capital. This assumes no systematic risk for cash outflows. Now, what is the value of this project? If management decides to commit to both stages immediately, then we could perform a simple net present value analysis. However, if management has the flexibility to decide in two years whether to commercialize the project, we will need to use a real options analysis. Let's start with a net present value analysis. First, we need to calculate the discounted cash flows. The discounted cash flow, is the cash flow multiplied with the appropriate discount factor. Thus, we will use the risk-free rate for cash outflows and the opportunity cost of capital for the cash inflows. For example, the discounted cash flow of year two is equal to minus 1,600 divided by 1.02 to the power two. For example, the discounted cash flow of year three is equal to 400 divided by 1.16 to the power three. This provides us with the following discounted cash flows: minus 20, minus 98, minus 1,538, 256, 442, 571 and 123. These are rounded discounted cash flows. The present value of our cash outflows is in total minus 1,656, and the present value of our cash inflows is equal to 1,392.56. If we sum up these two values, then this leads to a negative NPV of minus 263.35. Based on this analysis, management should therefore not invest in the project. However, let's now consider the scenario in which management can invest in R&D stage first, but does not have to commit to the commercialization phase right now. That is, in two years at t=2, management has the option to invest in the commercialization phase when the circumstances are right. Suppose that V, the expected future cash inflows may fluctuate and the up and down factors are respectively 1.4 and 0.7 per period, we further assume the same risk-free rate as before. Finally, we assume that the risk-neutral probability is equal to 0.457. For our real options analysis, we will first calculate the value of the project at maturity, then we will determine the optimal decisions at the end nodes. We will do that by calculating the payoff of the options at each end node. Next, we calculate the present value of the option by working backwards with a risk-neutral probability. Finally, we can calculate the expanded net present value. We will begin with calculating the value at the end nodes. Know from our net present value analysis that the value of the expected future cash inflows from the commercialization phase, is equal to 1,392.56 at t=0. That is, V0 is equal to 1,392.56. In the next period, this value can go up to V times u, which gives us 1,392.56 times 1.4, which is equal to 1,949.58, or the value can go down to V times d, which gives us 1,392.56 times 0.7, which is then equal to 947.79. In period two, we follow the same reasoning that V can go either up or down, which gives us the following values at the end nodes: 2,729.42 in the up-up state, 1,364.71 in the up-down or down-up state, and 682.35 in the down-down state. Next, we're going to determine the optimal decisions at maturity. Management has decide whether or not to commercialize the project, that is, to exercise the option to invest. For an option to invest, the payoff at the end node is the maximum of the value of the project, V, minus the investment cost, I, and zero. In the up-up state, this is equal to the max of 2,729.42 minus 1,600, and zero. This is equal to 1,129.42. In this state management will therefore decide to invest. In the other states however, the value is negative, and therefore management will not invest in the commercialization phase. The value of the option is equal to zero. To obtain the values in the previous periods, we work backwards from the payoff values at the end nodes. We apply the following formula: F in the previous period is the risk-neutral probability times F-up, plus one minus the risk-neutral probability times F-down, divided by one plus the risk-free rate. Remember that the values at the end nodes are 1,129.42, and zero, and zero. Thus for example, for this node over here, the value is 0.457 times 1,129.42, plus one minus 0.457 times zero, divided by 1.02, which is equal to 506.02. For the other points, this leads to zero and 226.72. However, at t=0, management still has to decide whether or not to start the R&D phase. Management will decide to start the R&D phase if the value of the total program is positive. The value of the program is the max of the value of the commercialization phase minus the present value of the required R&D expenditures and zero. The present value of the R&D expenditures at t=0 is equal to 20 plus 100 divided by 1.02, which is 118.04. The value of the program is then the max of 226.72 minus 118.04, and zero. This is equal to 108.68. Management will therefore decide to invest in the R&D phase since the value is positive. Finally, the expanded net present value is the static net present value plus the option value. In this example, the static net present value is equal to minus 263.35. The expanded net present value is equal to the value of the program, which is equal to 108.68. The option value is therefore the difference between the expanded net present value and the static net present value. In this example, the option value is therefore equal to 372.03. Thank you for watching this video. If you have any questions or comments, please let us know.