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Wize University Introduction to Finance Textbook > Time Value of Money

Forward and Backward Starting Cash Flows

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Forward and Backward Starting Cash Flows

Cashflows typically start at t=0, but in some cases, they do not, solving these requires a bit more work.
  • Cash flow that does not start at t=0
  • Can start before t=0 (backward starting) or after t=0 (forward starting)

Computing the Present Value of a Forward or Backward Starting Cash Flow

Step 1: Compute the present value at the start of the cash flow
Step 2: Discount or compound the present value to the desired time period


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Example: Forward Starting Cash Flow

Find the present value of a 6-year annuity starting at the end of year 7. The annuity will pay $100 per year for 10 years and the APR is 10% compounded semi-annually.
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Practice: Forward Starting Cash Flow

You are considering investing $5,000 into a new project that your friend told you about. The investment will pay you $800 per year for 10 years but the first payment will not be received until the end of year 4. If the effective annual rate is 5%, should you make this investment?
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Example: Backward Starting Cash Flow

An investment will pay you $500 every 2 years, starting one year from today. What is the present value of the investment if your opportunity cost is 10% per year?

Practice: Backward Starting Cash Flow

You will receive a payment of $X every three years starting one year from today. The present value of your investment is $2,400 and the interest rate is 8% compounded monthly. What is the value of X?

Round the effective rates to at least 6 decimal places and the final answer to 2 decimal places.
Extra Practice
You would like to set up a scholarship at your university. Five years from today, you would like to award the first scholarship of $10,000 and each year thereafter the amount awarded will increase by 5% to account for inflation.
How much should you donate the university today assuming it can earn a return of 10% compounded quarterly.
What is the value of x if the present value of this cash flow is $500? The discount rate is 9% per year.
Round your work to at least 6 decimal places and final answer to 2 decimal places.
The following cash flow will continue forever and has a present value of $809.11. If the discount rate is 12% per year, what is the value of x?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
The following cash flow will continue forever and has a present value of $1094.44. If the discount rate is 10% per year, what is the value of x?
Round your work to at least 6 decimal places and final answer to 2 decimal places.
If you want to be able to withdraw $100,000 at the beginning of each year, starting in year 30. If your account earns 7.5% interest compounded quarterly, how much should you deposit into your account today?
Round your work to at least 6 decimal places and your final answer to 2 decimal places.
If you want to be able to withdraw $80,000 per year forever starting 30 years from now, how much should you deposit into your retirement account today if your account earns 8% interest per year?
An investment you made will begin paying you $1,000 per year for 5 years, starting at the end of year 2. The payments will increase to $7,000 per year thereafter and continue indefinitely. What is the present value of this investment if your opportunity cost is 5% per year?
You are trying to set up a scholarship for your university. You wish to donate an amount today that will be enough to pay for a students tuition each year forever. Tuitions next year are expected to be $10,000 per student, this number is expected to increase by 2% per year for the following 4 years. The university has announced that a government subsidy starting in year 6 will cause tuition fees to begin declining by 6% per year indefinitely, starting in year 6. Assuming the appropriate discount rate is 8% per year, how much should you donate today?
An investment will pay $x every 2 years starting at the end of year 3 and the payments will continue forever. The present value of the investment is $245 and the discount rate is 8% per year. What is the value of the payment x?
An annuity will pay $50 every 3 years starting at t=1 and will make 10 payments in total. If the effective annual rate is 10%, what is the present value of the annuity?
An investment will pay $500 per year forever starting in year 3. The discount rate is 8%, what is the present value?