R Tutorial : Valuation

Key Takeaways

with a constant interest i and corresponding discount factor V calculations are pretty simple you will now learn more general notation and setting that is fundamental to go beyond the constant interest rate and to incorporate interest rates that may change over time let's fix two time points s and T and introduce the notation V as T for the value at time s of 1 euro at time T the second argument T refers to the point in time when you consider the 1 euro if the first argument s is smaller than T then VST is a discounting factor but if s is larger than T then vs t is an accumulation factor such that 1 euro at T close to VST euro at time s let's assume an interest rate of 3 percent the corresponding discount factor V is 1 over 1 plus I in the first example set s to 2 and T 2 for V 2 for is then the value at time 2 of 1 euro at time 4 that's 0.94 euro you can calculate this value in two equivalent ways the discount factor V to the power 2 or 1 plus the interest rate I to the power minus to the power 2 in our example corresponds to the number of time units that elapses between time points s and D in the second example set s to 6 and T 2 3 then V 6 3 tells you how one euro at time 3 close to 1.09 euro at time 6 you now have a general mechanism to value a cash flow vector at any point in time you convert each cash flow CK in the vector from time k to time n using discount factor V and gay the sum over all entries in the vector then gives you the value at time n when n is equal to zero you obtain the present value of the cash flow vector when n is equal to capital n the time point that corresponds to the last entry in the vector you obtain the vectors accumulated value let's do this in our you face a cash flow of five hundred zero at time zero three hundred zero at time two and two hundred zero at times seven what is the value of this cash flow vector at time three you create a function discount with three arguments s T and I the interest rate I has a default value of 0.03 or three percent the function returns 1 plus I raised to the negative time difference between T and s thus when T is larger than s the function discounts one euro at time T to time s and when s is larger than T the function accumulates one euro at time T to time pass using this function you convert the cash flows in the time line to time three with an interest rate of three percent the value at time three is thousand thirty three euro instead of repeatedly using the discount function you can vectorize this code you call the function discount with first argument s equal to three the point in time at which you want to value the cash flows the second argument is now a vector running from zero to seven the points considered on the time line thus the vectorized function call returns a vector with the values at time three of one euro at time zero to seven multiplying with the vector cash flows and taking the sum returns the value of the given cash flows at time three that's again thousand thirty three euro now you're ready for some cash flow valuation in our