Savings and PMT/NPER/PV/FV - Two-Stage Problems (Video Notes Review)

Flashcards cover key concepts from the lecture notes on savings problems using PMT, FV, PV, NPER, and two-stage cash-flow scenarios, including sign conventions, timing (beginning vs end of period), quarterly compounding, Excel nuances, and related financial formulas.

In the described savings problem, what does the PMT pattern represent when the first payment is one year from today?

Annual deposits made one year from today (end-of-period deposits).

What does FV represent in this two-stage savings scenario?

The amount your daughter will need on the day she enters college.

Why is PV often set to 0 in the stage that funds FV with PMT, and what rate is used?

PV = 0 because you start from zero savings; use 6% as the interest rate for that stage.

If college entry is 5 years from today and the daughter will enter at age 18, how old is she today?

13 years old.

How are the two timelines connected in a two-stage savings problem?

They connect at the college-entry date, linking the FV target to the PV of withdrawals; today is the start of the left timeline.

What sign convention makes the PV positive when using PMT to accumulate toward FV?

Make the PMT negative (deposits treated as outflows); PV will come out positive.

Which function determines how many years (periods) pass from today until college entry?

The NPER function computes the number of periods until the target date.

Why must PMT and FV be opposite signs in a two-stage savings problem?

Because the two cash flows are in opposite directions from the account’s perspective (deposits vs. goal withdrawals).

When interest is 8% per year but compounded quarterly, what per-period rate and number of periods should you use?

Rate per quarter = 0.08/4 = 0.02; number of periods equals the number of quarters in the horizon (e.g., 4 per year).

What happens to the first-stage rate if the Audi’s appreciation rate changes from 10% to 9% annually in the two-stage example?

The first-stage rate changes (to 9%); the reduced-form approach becomes incorrect and you must recompute with the two-stage model.

How do you compute the present value of a 25,000 cash flow due in one year with 8% annual rate compounded quarterly?

Rate per quarter = 0.08/4; periods = 4; PV = -FV / (1 + 0.08/4)^4 (signs depend on perspective).

What is a key Excel nuance when discounting a stream with nonstandard timing using NPV?

Excel assumes the first cash flow occurs in year 1; if timing differs, insert a leading 0 or adjust inputs so timing is accurate.

How can you interpret a two-stage problem involving a 70,000/year withdrawal for four years starting at the college day?

Treat the withdrawals as a beginning-of-year annuity (type = 1) for four years, with PV calculated at the college day.

What is the formula for the present value of a four-year annuity of 70,000 per year paid at the beginning of each year at 5%?

PV ≈ 70,000 × [(1 − (1.05)^−4)/0.05 × (1+0.05)] ≈ 260,600 dollars.

What Excel timing issue can arise when using NPV for streams that start later than year 1, and how can you handle it?

Excel may treat the first cash flow as year 1; to reflect a later start, include a 0 in the first period or adjust the input sequence accordingly.

What is the general idea of the perpetuity rate problem described in the notes?

A perpetuity yields infinite cash flows; solve for the rate of return given price and cash flow using a rearranged formula.

In a two-stage problem where the first PMT occurs at the same time as PV (PV and PMT coincide), which PVF/PV function setting changes?

Set the type (payments at period start vs end) to reflect an annuity due pattern (type = 1).

Why might it be helpful to consider a two-stage model instead of a reduced-form single-rate model?

Because a reduced-form approach may be inaccurate if the rates or timing differ between stages; the two-stage model captures the true cash-flow structure.

What is the practical effect of using more decimal places for interest rates in these calculations?

More decimals improve accuracy and help avoid rounding errors that can affect the final results.