# Present value of 5% bond

#### davep3000

##### New Member
Hey, I was wondering if you guys could explain this to me.

On the 1st tab I have a situation where a \$100 bond pays coupon payments of \$5 (5% bond). I have 3 examples... a 1 year bond, a 2 year bond and a 3 year bond.

On that tab, I discount the cash flows at 5% and so I expect the NPV formula to give me \$0 (and it does). I expect the sum of the discounted cash flows to give me \$100 and they do

But on the 2nd tab I change the discount rate to 3%. As expected, the \$5 coupon bond trades at a premium. But what I don't understand is the NPV formula gives a slightly different result to the manual discounting columns (and the PV formula columns). That is indicated by the "Variance" on row 23.

The 3 year bond has a bigger variance than the 2 year which has a bigger variance than the 1 year.

Same thing when I use a 7% discount rate (3rd tab)

I'm wondering what I'm doing wrong / which is right - the NPV formula or the manual calc.

Can't download the mini-sheet software unfortunately but I can email you the file. Pretty easy to reconstruct...

#### Attachments

• bond variance.PNG
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### Excel Facts

How to fill five years of quarters?
Type 1Q-2023 in a cell. Grab the fill handle and drag down or right. After 4Q-2023, Excel will jump to 1Q-2024. Dash can be any character.

#### davep3000

##### New Member
so, I just had the idea of adding some dates and using the XNPV formula and I see that agrees with my manual recalc. So I guess there is something about the NPV formula that I don't understand

#### Attachments

• bond variance XNPV.PNG
54 KB · Views: 0

#### davep3000

##### New Member
I figured this out, I shouldn't have included the initial \$ - 100 CF in the NPV formula because Excel thinks that happens at the end of year 1 instead of at period zero.

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