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Problem 6: Calculate the present values at t = 0 (now) of the following cash flows: a. $100 every year forever, with the first payment at t = 1 (t counts years), where the effective annual rate is .05 (i.e., 5%). b. $100 every year forever, with the first payment at t = 11 (t counts years), where the effective annual rate is .05 (i.e., 5%). Hint: What will be the value of this stream at t = 10 (ten years from now) if the discount rate remains 5%? To get the value at t = 0, discount this single value back 10 years at 5%.

Problem 6: Calculate the present values at t = 0 (now) of the following cash flows: a. $100 every year forever, with the first payment at t = 1 (t counts years), where the effective annual rate is .05 (i.e., 5%). b. $100 every year forever, with the first payment at t = 11 (t counts years), where the effective annual rate is .05 (i.e., 5%). Hint: What will be the value of this stream at t = 10 (ten years from now) if the discount rate remains 5%? To get the value at t = 0, discount this single value back 10 years at 5%.

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Problem 6: Calculate the present values at t = 0 (now) of the following cash flows: a. $100 every year forever, with the first payment at t = 1 (t counts years), where the effective annual rate is .05 (i.e., 5%). b. $100 every year forever, with the first payment at t = 11 (t counts years), where the effective annual rate is .05 (i.e., 5%). Hint: What will be the value of this stream at t = 10 (ten years from now) if the discount rate remains 5%? To get the value at t = 0, discount this single value back 10 years at 5%. %3D
Transcribed Image Text:Problem 6: Calculate the present values at t = 0 (now) of the following cash flows: a. $100 every year forever, with the first payment at t = 1 (t counts years), where the effective annual rate is .05 (i.e., 5%). b. $100 every year forever, with the first payment at t = 11 (t counts years), where the effective annual rate is .05 (i.e., 5%). Hint: What will be the value of this stream at t = 10 (ten years from now) if the discount rate remains 5%? To get the value at t = 0, discount this single value back 10 years at 5%. %3D
c. $100 every year for 10 years, with the first payment at t=1 (t counts years), where the effective annual rate is .05 (5%). Calculate this value using the present value of an annuity formula. Compare this value to the value you get by subtracting your answer to b above from your answer to a above. Why are they related as they are? d. $100 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .05 (i.e., 5%). e. $1000 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .05 (i.e., 5%). $1000 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .10 (i.e., 10%). f. g. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .1 (10 %)? h. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .05 (5%)? i. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .035 (3.5%)? The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues for 9 years past the first payment (for a total of 10 payments). What is the present value of this growing annuity if the effective annual discount rate is .02 (2%)? k. $50 every year and a half forever, with the first payment after 1.5 years, where the effective annual rate is .05 (i.e., 5%).
Transcribed Image Text:c. $100 every year for 10 years, with the first payment at t=1 (t counts years), where the effective annual rate is .05 (5%). Calculate this value using the present value of an annuity formula. Compare this value to the value you get by subtracting your answer to b above from your answer to a above. Why are they related as they are? d. $100 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .05 (i.e., 5%). e. $1000 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .05 (i.e., 5%). $1000 every 3 years forever, with the first payment at t = 3 (t counts years), where the effective annual rate is .10 (i.e., 10%). f. g. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .1 (10 %)? h. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .05 (5%)? i. The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues on forever. What is the present value of this growing perpetuity if the effective annual discount rate is .035 (3.5%)? The first cash flow at t = 1 is $100. Every year thereafter, the payment increases by 3% over the previous year's payment. This continues for 9 years past the first payment (for a total of 10 payments). What is the present value of this growing annuity if the effective annual discount rate is .02 (2%)? k. $50 every year and a half forever, with the first payment after 1.5 years, where the effective annual rate is .05 (i.e., 5%).
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