# Using TVM calculator

A firm has \$4 million in bonds that mature in 4 years @ a fixed rate of 7.5% paid annually. The market price is \$98. The marginal tax rate is 35%. With the bond-yield plus method, what is the cost of equity assuming an add-on of 4%?

When I input the following:

[PV] - 98

[PMT] 7.5

[FV] 100

[N] = 4

I get a rate of 8.11% , the correct figure, but when I use

[PV] 98

[PMT] 7.5

[FV] - 100

[N] = 4

I get the incorrect rate of 7.09%. I recall from quant methods that you have to input either [PV] or [FV] with a - sign, but I don’t believe it mattered which one you made negative. Why am I getting different results here? Thanks!

If your FV is negative your PMT needs to also be negative to get 8.11%. They are both inflows and must be treated consistently.

Whenever I teach Level I Quant, I tell my candidates to decide on one viewpoint in TVM calculations and stick with it. You can take the viewpoint of the:

• Lender/bondholder
• Borrower/bond issuer

It doesn’t matter which viewpoint you take – in the sense that you can get the correct answer either way – but if you always take the same viewpoint, you won’t make silly mistakes.

If you take the lender/borrower viewpoint, then,

• PV is negative: you pay for the bond today, a cash outflow
• PMT is positive: you receive the coupon payments, cash inflows
• FV is positive: you receive the par value at maturity, a cash inflow

If you take the viewpoint of the borrower/bond issuer, then,

• PV is positive: you receive payment for the bond today, a cash inflow
• PMT is negative: you make the coupon payments, cash outflows
• FV is negative: you repay the par value at maturity, a cash outflow