Question

On 01.05 the company TGV acquired a 91-day certificate of deposit issued by PEKAO S.A. On 01.04 (date of issuance) the face value of the certificate was 1 000 000, coupon - 2,3%. The purchase price was calculated in a way to ensure that the company TGV, which planned to hold the certificate to maturity, could realize a yield on investment of 2,8% (ACT/365). On 18.05 it turned out that TGV experienced temporary liquidity problems. The CFO took the decision to sell the certificate. Please calculate the yield on investment for TGV, taking into account that on 18.05 the bank X which proposed to purchase the certificate offered the price of 1 001 559 PLN.

Answer 1

Face Value	1000000		23000
Coupon	2.30%		2093000
YTM	2.80%		5734.247
No of days	91 days
Int on certificate	1000000*2.30%*91/365
	5734.25
Certificate purchase price = PV of int + PV of face value
	5734.25/(1.028)^91/365 + 1000000/(1.028)^91/365
		998833.68
Purchase price of certificate is 998833.68 Pln
We have to now find the yield on investment if on 18.05.2018 the Bank X purchase the certificate
Int for 18 days on the certificate = 1000000*0.023*18/365
		1134.247
998833.68 = 1134.25/(1+r)^18/365 + 1001559/(1+r)^18/365
Assuming yield to maturity is 8.1344 we get
1134.25(1+0.081344)^18/365 + 1001559/(1+0.081344)^18/365
Hence yield to investment would be 8.1344%