The present value for cashflows of $8,000 at the end of the 4th year and $70,000 at the end of the 13th year with a 10% discount rate is approximately $26,093.48. The calculations are based on the present value formula applied to each cash flow and then summed up. An increase in the discount rate leads to a decrease in the present value of future cashflows.
To determine the present value of the cashflow, consisting of $8,000 at the end of the 4th year and $70,000 at the end of the 13th year with a discount rate of 10%, we can use the present value formula for each cash flow separately and then sum them up. The formula for the present value (PV) of a future sum of money is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods until payment.
For the $8,000 payment at the end of the 4th year: PV = $8,000 / (1 + 0.10)^4 = $8,000 / 1.4641 = $5,465.84 (approximately).
For the $70,000 payment at the end of the 13th year: PV = $70,000 / (1 + 0.10)^13 = $70,000 / 3.3936 = $20,627.64 (approximately).
Therefore, the total present value of both cashflows is $5,465.84 + $20,627.64 = $26,093.48 (approximately).
Using the reference information, we see that an increase in the discount rate decreases the present value of future cashflows. In the bond example provided, with an initial discount rate at 8%, the present value of two years of interest payments of $240 each, plus the principal of $3,000, calculated separately, would be combined to determine the bond's current value. If the discount rate increases to 11%, these same payments have a lower present value due to the higher discount rate illustrating the inverse relationship between discount rates and present values.