I'm going to go out on a limb here and guess that you have more than R1 in walls. Just the siding and interior gypsum on an uninsulated studwall would add up to R1. An uninsulated CMU wall is also about R1. Is it 2x4, or is it 2x6 framing, or something else?
What's the total amount of wall area you are renovating, after subtracting out windows & doors?
In almost all instances if you're starting out with 2x4 walls adding another R7.5-10 on the exterior would be "worth it" in a Chicago-land climate (US zone 5) on a couple of levels- the first being raw creature-comfort on cold days/nights, due to a much warmer wall temperature on the interior side of those exterior walls. Perfectly installed R13 batts in 2x4 framing the "whole wall" R only ~ R10 after the thermal bridging of all the framing is factored in, with R11 batts you're looking at ~R9. In "typical" installations with some gaps & compressions, a few voids, performance is more like R8ish, so the exterior foam is roughly doubling the R value, cutting the conducted heat loss through the wall in half. More than that it cuts the difference in wall temperature from the average room temperature in half: In a 70F room where the exterior wall HAD been an average of ~65-66F when it's 0F outside, with the exterior foam it would now run ~68F, and that's a difference you can FEEL.
With 2x6 framing it makes a difference too, but not a dramatic a difference. The whole-wall R of typical 2x6 construction is about R14, so adding R7.5 would cut the temperature difference between room air and exterior walls by about a third. Where the wall temp might have been ~66-67F at 0F outdoor temps now you're looking at ~68F+. Adding the R10 would make the wall a half-degree or so warmer than with the R7.5, a more subtle difference but still discernable if you have sections of R20-R24 whole wall adjacent to sections of R14.
With either framing the biggest difference of foam/no-foam would be felt at the cool-striping of the framing elements, which had been much colder than the average wall temp. Adding R7-10 to an R4-6 thermal-short makes for a more uniform radiation temperature of the wall. This is usually only noticeable if you're standing fairly close to the wall, or touching it, but you won't need an infra-red imaging camera to tell the difference. Once you're at ~R20 for a whole wall R the difference in comfort at ever higher R is much less noticeable unless you live in a much colder climate than yours. In Fairbanks or Whitehorse I can imagine the difference between R20 and R40 walls could be an obvious comfort upgrade, but not in Wilmette. There's still a lifecycle-cost longer term economic argument for up to ~R30 walls in your climate, but unless you're looking at the net-present value of another R10 above R20 over 25 years or more it's not going to be "worth it" on strictly financial terms.
From a utility savings point of view it depends on how you are heating the place- what fuel, the fuel cost, and the efficiency rating of the heating equipment, but it's pretty straighforward math from there using the wall area, whole-wall U-value (=1/whole-wall R) and the heating degree days for a typical season (~6500HDD, for Wilmette.) 6500 heating degree days, is (24 x 6500=) 156,000 heating degree-hours. An R10 wall (2x4 fiber-insulated) has a U-value of (1/R10=) 0.1 BTUs per hour per degree per square foot, so over and entire the heating season each square foot of wall area loses approximately (0.1 x 156,000)=15,600 BTUs If the heating is supplied by an 80% gas furnace or boiler it takes (15,600/0.8=) 19,500 BTUs of source-fuel, or ~0.2 therms/year per square foot of wall area. If you double the R, that's cut to ~0.1 therms/foot, so you've saved 0.1 therms. If you're upgrading a 20' x 10' section of wall, that has three 10' square foot windows, that's 170 square feet of wall area, and 17 therms of fuels savings. At about 10cent/R per foot (EPS or rigid iso costs) adding R10 to 170' of wall area is still 10 year payout in simple-terms at a buck a therm, but if the price of fuel increases in that time frame it's still a reasonable investment. With 2lb foam it's more like 16-17cents/R-foot, maybe even 20 cents for very small jobs, but say it's 16 cents, that R10 costs you ~$272 and saves you $17/year- about a 6% internal rate of return (after taxes too!), which isn't terrible, but unless you can recoup the savings at time of resale or sticking around a coupla decades, if your definition of "worth it" is strictly financial, it may be at odds with performance, unless fuel price inflation steps up. (Mind you, the financial analysis of high-R walls is a lot more favorable when heating with oil or propane.)
Mind you, code min in northern IL is R20 cavity insulation in 2x6 framing (=R14 whole wall) or R5 sheathing over R13 in 2x4 framing (=R15 whole-wall), so if you have 2x4 framing you'll be on the hook for R5 no matter what, and the labor costs of R5 vs. R7.5 vs. R10 are pretty much the same- going R10 isn't 2x the cost of going the code-require R10. The higher comfort level of an R20+ wall in at US zone 5 climate is "worth it" my book, even if the net-present-value on only 5-6 years of utility savings isn't positive. YMMV.
But I may have completely misconstrued your wall construction- you tell me!?!
BTW: If you're opening up the studwall cavities (or even if you're not), it's worth packing in cheap cellulose in there, compressing the older batts or whatever. Blown insulation will fill every void and crack, and "finds" and fills the air leaks in the cavity during insulation, making a much more air-tight wall, with a stable R value. Low density batts don't perform to spec at the temperature extremes due to convection currents within the batt, and does very little to impede infiltration air flows. |