Swaps + Bonds

Swaps Interest rates could change over time , investors may consider entering a swap To get constant rate (Swap rate) on their investments.

Swaps 𝑌𝑒𝑎𝑟 1 4% 𝑅 𝑌𝑒𝑎𝑟 2 5% 𝑌𝑒𝑎𝑟 3 6% Floating / Changing Rates Constant / Swap Rates 𝑌𝑒𝑎𝑟 1 4% 𝑅 𝑌𝑒𝑎𝑟 2 5% 𝑌𝑒𝑎𝑟 3 6%

PV of Interest payments PV of Interest payments Swaps PV of Interest payments By changing rates PV of Interest payments By the Swap rate =

PV of Interest payments Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔: 𝒇 𝟎,𝟏 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏 𝒇 𝟏,𝟐 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐 𝒇 𝟐,𝟑 ∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑 PV of Interest payments By changing rates

PV of Interest payments Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔: 𝟎.𝟎𝟒∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 =𝟐,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏 𝟎.𝟎𝟔𝟎𝟎𝟗𝟔𝟐∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎=𝟑,𝟎𝟎𝟒,𝟖𝟏𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐 𝟎.𝟎𝟖𝟎𝟐𝟖𝟔𝟔∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎=𝟒,𝟎𝟏𝟒,𝟑𝟑𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑 𝑃𝑉= 0.04∙50,000,000 1.04 + 0.0600962∙50,000,000 1.05 2 + 0.0802866∙50,000,000 1.06 3 = 2,000,000 1.04 + 3,004,810 1.05 2 + 4,014,330 1.06 3 PV of Interest payments By changing rates

PV of Interest payments Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 𝑃𝑉= 0.04∙50,000,000 1.04 + 0.0600962∙50,000,000 1.05 2 + 0.0802866∙50,000,000 1.06 3 𝑃𝑉=50,000,000 0.04 1.04 + 0.0600962 1.05 2 + 0.0802866 1.06 3 PV of Interest payments By changing rates

PV of Interest payments Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔: 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑 PV of Interest payments By the Swap rate

PV of Interest payments Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒑𝒂𝒚𝒎𝒆𝒏𝒕𝒔: 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟏 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟐 𝑹∙𝟓𝟎,𝟎𝟎𝟎,𝟎𝟎𝟎 𝒊𝒏 𝒚𝒆𝒂𝒓 𝟑 𝑃𝑉= 𝑅∙50,000,000 1.04 + 𝑅∙50,000,000 1.05 2 + 𝑅∙50,000,000 1.06 3 𝑃𝑉=50,000,000 𝑅 1.04 + 𝑅 1.05 2 + 𝑅 1.06 3 PV of Interest payments By the Swap rate

Example 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 50,000,000 3−𝑦𝑒𝑎𝑟 𝑙𝑜𝑎𝑛 , 𝑤𝑖𝑡ℎ 𝑠 1 4% , 𝑠 2 =5% , 𝑠 3 =6%. 50,000,000 0.04 1.04 + 0.0600962 1.05 2 + 0.0802866 1.06 3 =50,000,000 𝑅 1.04 + 𝑅 1.05 2 + 𝑅 1.06 3 0.04 1.04 + 0.0600962 1.05 2 + 0.0802866 1.06 3 =𝑅∙ 1 1.04 + 1 1.05 2 + 1 1.06 3 𝑅=0.059221

Example (Faster Approach) 𝑊𝑒 𝑐𝑎𝑛 𝑤𝑜𝑟𝑘 𝑎𝑠 𝑤𝑒 ℎ𝑎𝑣𝑒 𝑎 𝑏𝑜𝑛𝑑 𝑤𝑖𝑡ℎ 𝐹=1 , 𝐶=1 ,𝑃=1 , 𝑟=𝑅 𝑃=𝐹𝑟∙ 𝑎 𝑛 +𝐶 𝑣 𝑛 1=1∙𝑅∙ 1 1.04 + 1 1.05 2 + 1 1.06 3 +1∙ 1 1.06 3 𝑅=0.059221

BONDS Introduction THERE ARE TWO WAYS FOR A CORPORATION TO RAISE CAPITAL ISSUE DEPT COMMENLY BONDS ISSUE EQUITY COMMENLY STOCKS

WHAT IS A BOND? A BOND IS A LOAN BORROWS FROM BOND ISSUER (BORROWER) INVESTOR (LENDER)

BONDS PAYS COUPONS REDEMPTION VALUE SYSTIMATIC INSTALLMENTS CALLED A FINAL BALLOON PAYMENT CALLED REDEMPTION VALUE

BONDS - TERMENOLOGY r – COUPON RATE PERCETAGE OF THE FACE AMOUNT F – FACE AMOUNT COUPONS ARE CALCULATED BASED ON IT C – REDEMPTION VALUE FINAL PAYMENT Fr – COUPON AMOUNT (SYSTIMATIC PAYMENTS) r – COUPON RATE PERCETAGE OF THE FACE AMOUNT

Example To fund a project the government issues a block of bonds each has a coupon rate of 6% convertible semiannually for 5 years and pays 1000 at redemption where 𝒊 (𝟐) =𝟒%. 𝑭=𝑪=𝟏𝟎𝟎𝟎 𝒓= 𝟔% 𝟐 =𝟑% 𝑭𝒓=𝟑𝟎

BONDS ARE LOANS IN LOANS : IN BONDS : 𝑳𝑶𝑨𝑵 𝑨𝑴𝑶𝑼𝑵𝑻 = 𝑻𝑯𝑬 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑨𝑳𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺 IN BONDS : 𝑷𝑹𝑰𝑪𝑬 𝑶𝑭 𝑨 𝑩𝑶𝑵𝑫 = 𝑻𝑯𝑬 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑨𝑳𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺 =𝑷𝑹𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑪𝑶𝑼𝑷𝑶𝑵𝑺 + 𝑷𝑹𝑺𝑬𝑺𝑬𝑵𝑻 𝑽𝑨𝑳𝑼𝑬 𝑶𝑭 𝑻𝑯𝑬 𝑹𝑬𝑫𝑬𝑴𝑷𝑻𝑰𝑶𝑵 𝑽𝑨𝑳𝑼𝑬

REMEMBER LOANS 𝐋=𝐀 𝑎 𝑛 𝑨𝑺𝑺𝑼𝑴𝑬 𝒏−𝒀𝑬𝑨𝑹 𝑳𝑶𝑨𝑵 𝑾𝑰𝑻𝑯 : 𝑨𝑵𝑵𝑼𝑨𝑳 𝑷𝑨𝒀𝑴𝑬𝑵𝑻𝑺 𝑶𝑭 𝑨 𝑨 𝑨 𝑨 𝑨 𝑨 … … … 0 1 2 3 n-1 n 𝐋=𝐀 𝑎 𝑛

Back to BONDS C Fr Fr Fr Fr Fr … … … 0 1 2 3 n-1 n 𝑃=𝐹𝑟 𝑎 𝑛 +𝐶 𝑣 𝑛

Bonds Pricing - Example To fund a project the government issues a block of bonds each has a coupon rate of 6% convertible semiannually for 5 years and pays 1000 at redemption where 𝒊 (𝟐) =𝟒%. 𝑭=𝑪=𝟏𝟎𝟎𝟎 𝒓= 𝟔% 𝟐 =𝟑% 𝑭𝒓=𝟑𝟎 𝑃=𝟑𝟎 𝑎 𝟏𝟎 𝟒% +𝟏𝟎𝟎𝟎 𝑣 𝟏𝟎